A029065 Expansion of 1/((1-x)*(1-x^4)*(1-x^5)*(1-x^8)).

1, 1, 1, 1, 2, 3, 3, 3, 5, 6, 7, 7, 9, 11, 12, 13, 16, 18, 20, 21, 25, 28, 30, 32, 37, 41, 44, 46, 52, 57, 61, 64, 71, 77, 82, 86, 94, 101, 107, 112, 122, 130, 137, 143, 154, 164, 172, 179, 192, 203, 213, 221, 235, 248

Offset

0,5

Comments

Number of partitions of n into parts 1, 4, 5 and 8. - Ilya Gutkovskiy, May 17 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,0,-1,0,1,-2,1,0,-1,0,1,0, 0,1,-1).

Formula

a(n) = a(n-1)+a(n-4)-a(n-6)+a(n-8)-2*a(n-9)+a(n-10)-a(n-12)+a(n-14)+a(n-17)-a(n-18). - Wesley Ivan Hurt, May 17 2021

a(n) = floor((n^3 + 27*n^2 + 239*n + 975)/960 - ((n+1)/64)*((n mod 4)-1)^2). - Hoang Xuan Thanh, Jul 30 2025

Mathematica

CoefficientList[Series[1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^8)), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)

Prog

(PARI) my(x='x+O(x^50)); Vec(1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^8))) \\ G. C. Greubel, May 17 2017
(PARI) a(n) = (n^3 + 27*n^2 + 239*n + 975 - 15*(n+1)*((n%4)-1)^2)\960 \\ Hoang Xuan Thanh, Aug 11 2025

Crossrefs

Sequence in context: A130499 A020910 A374022 * A263253 A376530 A162157

Adjacent sequences: A029062 A029063 A029064 * A029066 A029067 A029068

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved