/**
* @module sequences
*/
// Generalized pentagonal numbers
// https://oeis.org/A001318
const getGpn = (zero, one, two, three) => {
const gk = k => k * (three * k - one) / two;
return n => {
const m = (n + one) / two | zero;
return n % two === zero ? gk(-m) : gk(m);
};
};
/**
* Generalized Pentagonal Numbers (GPN).
* Formula: P_k = k(3k - 1) / 2
* The sequence includes k = 0, 1, -1, 2, -2, 3, -3...
* https://oeis.org/A001318
* @param {number} n - The index of the sequence (0-based).
* @returns {number} The n-th generalized pentagonal number.
* @see {@link https://instacode.app/run/FASwtgDg9gTgLgAgN4IOYQHYIL4IGYxRgIBEAAqgNYCuAxmCAKYwBeA9NXCADYDOJAbmDB0GIUA|▶ Try it live in Instacode}
*/
export const gpn = getGpn(0, 1, 2, 3);
/**
* Generalized Pentagonal Numbers (GPN) - BigInt version.
* @param {bigint} n - The index of the sequence (0-based).
* @returns {bigint} The n-th generalized pentagonal number.
* @see {@link https://instacode.app/run/FASwtgDg9gTgLgAgN4IOYQHYCECSCC+CAZjFGAgEQACqA1gK4DGYIApjAF4D09cIANgGcKAbmDB02HGKA|▶ Try it live in Instacode}
*/
export const gpnBI = getGpn(0n, 1n, 2n, 3n);