A029298 - OEIS

A029298

Expansion of 1/((1-x^3)*(1-x^6)*(1-x^8)*(1-x^10)).

1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 1, 1, 3, 1, 2, 3, 3, 2, 5, 3, 4, 5, 5, 4, 8, 5, 7, 8, 8, 7, 12, 8, 11, 12, 12, 11, 17, 12, 16, 17, 18, 16, 23, 18, 22, 23, 25, 22, 31, 25, 30, 31, 33, 30, 40, 33, 40, 40, 43, 40, 51, 43, 51, 51, 55

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OFFSET

0,7

COMMENTS

Number of partitions of n into parts 3, 6, 8, and 10. - Hoang Xuan Thanh, Apr 07 2026

LINKS

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

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

FORMULA

a(n) = floor((n^3+45*n^2+456*n+2338)/8640 - (n mod 2)*(n^2+27*n)/960 + ((2*n^2+1) mod 3)*(n+12)/18 + ((3*n^3+3*n+1) mod 5)/5 - ((n+1) mod 3)/54). - Hoang Xuan Thanh, Apr 07 2026

MATHEMATICA

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^8)(1-x^10)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

LinearRecurrence[{0, 0, 1, 0, 0, 1, 0, 1, -1, 1, -1, 0, -1, -1, 0, -1, 1, -1, 1, 0, 1, 0, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 1, 1, 3, 1, 2, 3, 3, 2, 5, 3, 4, 5, 5, 4, 8, 5, 7}, 70] (* Harvey P. Dale, Mar 06 2023 *)

PROG

(PARI) Vec(1/((1-x^3)*(1-x^6)*(1-x^8)*(1-x^10)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 07 2026

CROSSREFS

Sequence in context: A367771 A334152 A092130 * A262520 A351074 A394026

Adjacent sequences: A029295 A029296 A029297 * A029299 A029300 A029301

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved