Lucas

Compute the nth Lucas number.

The Lucas numbers are the integer sequence

$$2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, \ldots$$

The sequence is defined by the recurrence relation

$$L_n = \begin{cases}2 & \textrm{if}\ n = 0\\1 & \textrm{if}\ n = 1\\L_{n-1} + L_{n-2} & \textrm{if}\ n > 1\end{cases}$$

Usage

var lucas = require( '@stdlib/math/base/special/lucas' );

lucas( n )

Computes the nth Lucas number.

var v = lucas( 0 );
// returns 2

v = lucas( 1 );
// returns 1

v = lucas( 2 );
// returns 3

v = lucas( 3 );
// returns 4

v = lucas( 76 );
// returns 7639424778862807

If n > 76, the function returns NaN, as larger Lucas numbers cannot be safely represented in double-precision floating-point format.

var v = lucas( 77 );
// returns NaN

If not provided a nonnegative integer value, the function returns NaN.

var v = lucas( 3.14 );
// returns NaN

v = lucas( -1 );
// returns NaN

If provided NaN, the function returns NaN.

var v = lucas( NaN );
// returns NaN

Examples

var lucas = require( '@stdlib/math/base/special/lucas' );

var v;
var i;

for ( i = 0; i < 77; i++ ) {
    v = lucas( i );
    console.log( v );
}

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C APIs

Usage

#include "stdlib/math/base/special/lucas.h"

stdlib_base_lucas( n )

Computes the nth Lucas number.

double out = stdlib_base_lucas( 0 );
// returns 2

out = stdlib_base_lucas( 1 );
// returns 1

The function accepts the following arguments:

• n: [in] int32_t input value.

double stdlib_base_lucas( const int32_t n );

Examples

#include "stdlib/math/base/special/lucas.h"
#include <stdio.h>
#include <stdint.h>

int main( void ) {
    int32_t i;
    double v;

    for ( i = 0; i < 77; i++ ) {
        v = stdlib_base_lucas( i );
        printf( "lucas(%d) = %lf\n", i, v );
    }
}

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See Also

• @stdlib/math/base/special/fibonacci: compute the nth Fibonacci number.
• @stdlib/math/base/special/negalucas: compute the nth negaLucas number.