A029257 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^7)*(1-x^8)).

1, 0, 0, 1, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 4, 5, 5, 4, 6, 7, 7, 7, 9, 10, 11, 10, 12, 14, 15, 14, 17, 19, 20, 19, 22, 25, 26, 25, 29, 32, 33, 32, 37, 40, 41, 41, 46, 49, 51, 51, 56, 60, 62, 62, 68, 72, 75, 75, 81, 86, 89, 89

Offset

0,8

Comments

Number of partitions of n into parts 3, 4, 7, and 8. - 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 (0,0,1,1,0,0,0,1,0,-1,-2,-1,0,1,0,0,0,1,1,0,0,-1).

Formula

a(n) = floor((2*n^3+66*n^2+405*n+3582)/8064 + (-1)^n*(n+16)/128 + ((n^3+2*n+1) mod 4)*n/32 + ((3*n^3+n^2+2*n+4) mod 7)/7). - Hoang Xuan Thanh, Mar 22 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^7) (1 - x^8)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^7)*(1-x^8)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A131730 A029335 A384835 * A194258 A165927 A127830

Adjacent sequences: A029254 A029255 A029256 * A029258 A029259 A029260

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved