フィボナッチ列の計算

fibonacci_word_sequence_definition.js

const s = [];
s[0] = '0';
s[1] = '01';

function fibonacci_word(n) {
  let ret;

  if (n < 2) {
    ret = s[n];

    return ret;
  }

  ret = fibonacci_word(n - 1) + fibonacci_word(n - 2);

  s[n] = ret;

  return ret;
}

let num;

num = fibonacci_word(5);

console.log(num); // => 0100101001001

fibonacci_word_sequence_general.js

function fibonacci_word_sequence(n) {
  const { sqrt, floor } = Math;
  const φ = (1 + sqrt(5)) / 2;

  let ret;

  ret = 2 + floor((n + 1) * φ) - floor((n + 2) * φ);

  return ret;
}

const zeros = (n) => new Array(n).fill(0);

const arr = zeros(13).map( (_num, i) => fibonacci_word_sequence(i) );

console.log(arr); // => [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]

fibonacci_word_sequence_sort.js

const { sqrt, floor } = Math;
const φ = (1 + sqrt(5)) / 2;

const zeros = (n) => new Array(n).fill(0);

function fibonacci_word_sequence_array_with_length(n) {
  const gArr = zeros(floor((n + 1) / φ)).map( (_num, i) => (i + 1) / φ );

  const iArr = zeros(floor((n + 1) / φ / φ)).map( (_num, i) => i + 1 );

  const cuttingArr = gArr.concat(iArr);

  cuttingArr.sort( (a, b) => a - b );

  let ret;

  ret = cuttingArr.map( (num) => Number.isInteger(num) ? 1 : 0 );

  return ret;
}

let arr;

arr = fibonacci_word_sequence_array_with_length(13);

console.log(arr); // => [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]