A029359 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^9)).

1, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 1, 2, 4, 2, 2, 2, 4, 3, 3, 4, 6, 5, 4, 5, 7, 6, 6, 7, 10, 8, 8, 9, 12, 10, 10, 12, 15, 13, 13, 15, 18, 16, 16, 18, 22, 20, 20, 22, 26, 24, 24, 26, 31, 29, 29, 31, 36, 34, 34, 37, 42, 40

Offset

0,9

Comments

Number of partitions of n into parts 4, 7, 8, and 9. - Hoang Xuan Thanh, May 14 2026

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: 1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^9)).

a(n) = a(n-4) + a(n-7) + a(n-8) + a(n-9) - a(n-11) - a(n-12) - a(n-13) - a(n-15) - a(n-16) - a(n-17) + a(n-19) + a(n-20) + a(n-21) + a(n-24) - a(n-28). - Wesley Ivan Hurt, Feb 22 2025

a(n) = floor((n+38)*(n^2+4*n+100)/12096 + ((n mod 4)-2)^2*(n+16)/64 + (((n+1) mod 4) - (n mod 4))/64 + ((n mod 4)-2)*((n mod 8) - ((n+4) mod 8) + 2)/32). - Hoang Xuan Thanh, May 14 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^8)(1-x^9)), {x, 0, 80}], x] (* Harvey P. Dale, Oct 17 2011 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^9))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Crossrefs

Sequence in context: A029376 A276790 A366951 * A349815 A173389 A241062

Adjacent sequences: A029356 A029357 A029358 * A029360 A029361 A029362

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved