A029214 - OEIS

A029214

Expansion of 1/((1-x^2)*(1-x^6)*(1-x^7)*(1-x^8)).

1, 0, 1, 0, 1, 0, 2, 1, 3, 1, 3, 1, 4, 2, 6, 3, 7, 3, 8, 4, 10, 6, 12, 7, 14, 8, 16, 10, 19, 12, 22, 14, 25, 16, 28, 19, 32, 22, 36, 25, 40, 28, 45, 32, 50, 36, 55, 40, 61, 45, 67, 50, 73, 55, 80, 61, 88, 67, 95, 73, 103, 80

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OFFSET

0,7

COMMENTS

Number of partitions of n into parts 2, 6, 7, and 8. - Hoang Xuan Thanh, Oct 20 2025

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = floor((n^3+45*n^2+600*n+2176)/4032 - (n^2+23*n+111)*(n mod 2)/192 + ((3*n^3+2*n^2+n+4) mod 7)/7). - Hoang Xuan Thanh, Oct 20 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^2)(1-x^6)(1-x^7)(1-x^8)), {x, 0, 70}], x] (* Harvey P. Dale, Dec 18 2011 *)

PROG

(PARI) Vec(1/((1-x^2)*(1-x^6)*(1-x^7)*(1-x^8)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

CROSSREFS

Sequence in context: A379630 A344774 A029227 * A134460 A130158 A352930

Adjacent sequences: A029211 A029212 A029213 * A029215 A029216 A029217

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved