A029156 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^7)*(1-x^8)).

1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 9, 9, 11, 11, 13, 14, 16, 17, 20, 20, 23, 24, 27, 28, 32, 33, 37, 38, 42, 44, 48, 50, 55, 57, 62, 64, 70, 72, 78, 81, 87, 90, 97, 100, 107, 111, 118, 122, 130, 134, 143, 147

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 3, 7, and 8. - Hoang Xuan Thanh, Oct 04 2025

Links

Table of n, a(n) for n=0..57.

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

Formula

a(n) = floor((n^3+30*n^2+300*n+1568)/2016 - n*(n mod 2)/32 + ((n+2) mod 3)/9). - Hoang Xuan Thanh, Oct 04 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^7)(1-x^8)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 18 2020 *)

Prog

(PARI) my(x='x+O('x^60)); Vec(1/((1-x^2)*(1-x^3)*(1-x^7)*(1-x^8))) \\ Stefano Spezia, Oct 04 2025

Crossrefs

Sequence in context: A029031 A188666 A328090 * A387737 A241826 A237979

Adjacent sequences: A029153 A029154 A029155 * A029157 A029158 A029159

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved