A357533 a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/(n-4*k)!.

1, 1, 1, 1, 2, 3, 4, 5, 8, 13, 20, 29, 46, 77, 128, 205, 338, 581, 1012, 1733, 2990, 5293, 9536, 17117, 30778, 56165, 104108, 193621, 360662, 677693, 1289080, 2467373, 4735826, 9142837, 17814308, 34950245, 68835118, 136197581, 271384112, 544302973, 1096578410, 2218459013, 4513377436

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = (3 * a(n-1) + n * a(n-4) + 1)/4 for n > 3.

Prog

(PARI) a(n) = sum(k=0, n\4, (n-3*k)!/(n-4*k)!);

Crossrefs

Cf. A072374, A122852, A357532, A357570.

Sequence in context: A307971 A346073 A211696 * A152526 A330706 A162901

Adjacent sequences: A357530 A357531 A357532 * A357534 A357535 A357536

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 19 2022

Status

approved