149 lines
3.6 KiB
Markdown
149 lines
3.6 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2020 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Tribonacci
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> Compute the nth [Tribonacci number][tribonacci-number].
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<section class="intro">
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The [Tribonacci numbers][tribonacci-number] are the integer sequence
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<!-- <equation class="equation" label="eq:tribonacci_sequence" align="center" raw="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" alt="Tribonacci sequence"> -->
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<div class="equation" align="center" data-raw-text="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" data-equation="eq:tribonacci_sequence">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_sequence.svg" alt="Tribonacci sequence">
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<br>
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</div>
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<!-- </equation> -->
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The sequence is defined by the recurrence relation
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<!-- <equation class="equation" label="eq:tribonacci_recurrence_relation" align="center" raw="F_n = F_{n-1} + F_{n-2} + F_{n-3}" alt="Tribonacci sequence recurrence relation"> -->
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<div class="equation" align="center" data-raw-text="F_n = F_{n-1} + F_{n-2} + F_{n-3}" data-equation="eq:tribonacci_recurrence_relation">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_recurrence_relation.svg" alt="Tribonacci sequence recurrence relation">
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<br>
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</div>
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<!-- </equation> -->
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with seed values `F_0 = 0`, `F_1 = 0`, and `F_2 = 1`.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var tribonacci = require( '@stdlib/math/base/special/tribonacci' );
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```
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#### tribonacci( n )
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Computes the nth [Tribonacci number][tribonacci-number].
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```javascript
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var v = tribonacci( 0 );
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// returns 0
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v = tribonacci( 1 );
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// returns 0
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v = tribonacci( 2 );
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// returns 1
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v = tribonacci( 3 );
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// returns 1
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v = tribonacci( 63 );
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// returns 8607945812375585
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```
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If `n > 63`, the function returns `NaN`, as larger [Tribonacci numbers][tribonacci-number] cannot be safely represented in [double-precision floating-point format][ieee754].
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```javascript
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var v = tribonacci( 64 );
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// returns NaN
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```
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If not provided a nonnegative integer value, the function returns `NaN`.
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```javascript
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var v = tribonacci( 3.14 );
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// returns NaN
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v = tribonacci( -1 );
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// returns NaN
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```
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If provided `NaN`, the function returns `NaN`.
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```javascript
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var v = tribonacci( NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var tribonacci = require( '@stdlib/math/base/special/tribonacci' );
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var v;
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var i;
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for ( i = 0; i < 64; i++ ) {
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v = tribonacci( i );
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console.log( v );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[tribonacci-number]: https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers
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[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
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</section>
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<!-- /.links -->
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