A029334 - OEIS

A029334

Expansion of 1/((1-x^4)*(1-x^5)*(1-x^7)*(1-x^10)).

1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 3, 3, 2, 3, 3, 4, 5, 4, 5, 4, 7, 7, 6, 7, 8, 9, 10, 9, 11, 10, 13, 14, 13, 14, 15, 17, 19, 17, 20, 19, 23, 24, 23, 25, 26, 29, 31, 29, 33, 32, 37, 38, 38, 40, 41, 45, 48, 46, 50, 50, 56

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OFFSET

0,11

COMMENTS

Number of partitions of n into parts 4, 5, 7, and 10. - Hoang Xuan Thanh, Apr 19 2026

LINKS

Table of n, a(n) for n=0..64.

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

FORMULA

a(n) = floor((n^3+39*n^2+344*n+1500)/8400 - (n mod 2)*n/80 + ((4*n^2+4*n+2) mod 5)*n/50 + ((n mod 4)-2)^2/16 + ((2*n^3+n^2+2*n+4) mod 7)/7). - Hoang Xuan Thanh, Apr 19 2026

MATHEMATICA

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^7)(1-x^10)), {x, 0, 70}], x] (* Harvey P. Dale, Aug 12 2014 *)

PROG

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^7)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

CROSSREFS

Sequence in context: A318362 A390762 A213237 * A375825 A275078 A286478

Adjacent sequences: A029331 A029332 A029333 * A029335 A029336 A029337

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved