A029263 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^8)*(1-x^10)).

1, 0, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 5, 3, 5, 5, 7, 5, 7, 7, 10, 7, 10, 10, 13, 10, 14, 13, 17, 14, 18, 17, 22, 18, 23, 22, 28, 23, 29, 28, 34, 29, 36, 34, 42, 36, 44, 42, 50, 44, 53, 50, 60, 53, 63, 60, 71, 63, 74, 71, 83, 74, 87, 83, 96, 87, 101, 96

Offset

0,9

Comments

Number of partitions of n into parts 3, 4, 8, and 10. - Vincenzo Librandi, Jun 03 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((2*n^3+75*n^2+663*n+8640)/11520 + (-1)^n*(n^2+25*n)/1280 + ((n^2+n+2) mod 4)*n/64 + ((n^3+2*n^2+3*n+2) mod 4)/8 - ((n^3+3*n^2+2*n) mod 4)/8). - Hoang Xuan Thanh, Mar 24 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^8) (1 - x^10)), {x, 0, 70}], x] (* Harvey P. Dale, Aug 16 2012 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^8)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A027349 A053277 A078661 * A097575 A103273 A289120

Adjacent sequences: A029260 A029261 A029262 * A029264 A029265 A029266

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved