A029332 - OEIS

A029332

Expansion of 1/((1-x^4)*(1-x^5)*(1-x^7)*(1-x^8)).

1, 0, 0, 0, 1, 1, 0, 1, 2, 1, 1, 1, 3, 2, 2, 3, 4, 3, 3, 4, 6, 5, 5, 6, 8, 7, 7, 8, 11, 10, 10, 11, 14, 13, 13, 15, 18, 17, 17, 19, 23, 21, 22, 24, 28, 27, 27, 30, 34, 33, 34, 36, 41, 40, 41, 44, 49, 48, 49, 52, 58, 57, 58, 62

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OFFSET

0,9

COMMENTS

Number of partitions of n into parts 4, 5, 7, and 8. - Hoang Xuan Thanh, Apr 17 2026

LINKS

Table of n, a(n) for n=0..63.

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

FORMULA

a(n) = floor((n^3+36*n^2+236*n+2112)/6720 + n*((n mod 4)-2)^2/64 + ((n^3+n^2+n+2) mod 5)/5 + ((6*n^3+6*n^2+2*n+2) mod 7)/7). - Hoang Xuan Thanh, Apr 17 2026

MATHEMATICA

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^7)(1-x^8)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

LinearRecurrence[{0, 0, 0, 1, 1, 0, 1, 1, -1, 0, -1, -2, -1, 0, -1, 1, 1, 0, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 0, 1, 2, 1, 1, 1, 3, 2, 2, 3, 4, 3, 3, 4, 6, 5, 5, 6}, 70] (* Harvey P. Dale, Apr 29 2022 *)

PROG

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^7)*(1-x^8)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 17 2026

CROSSREFS

Sequence in context: A106348 A161092 A392670 * A358172 A344058 A134431

Adjacent sequences: A029329 A029330 A029331 * A029333 A029334 A029335

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved