A025813 - OEIS

A025813

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

1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, 3, 2, 4, 2, 4, 2, 5, 3, 6, 4, 6, 4, 7, 5, 8, 6, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15, 12, 17, 13, 18, 14, 19, 15, 21, 17, 22, 18, 23, 19, 25, 21, 27, 22, 28, 23, 30, 25, 32, 27, 33

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OFFSET

0,7

COMMENTS

Number of partitions of n into parts 2, 6, and 7. - Hoang Xuan Thanh, Aug 29 2025

LINKS

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

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

FORMULA

a(n) = floor((n^2 + 15*n + 7*(n+8)*(-1)^n + 119)/168). - Hoang Xuan Thanh, Aug 29 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^2)(1-x^6)(1-x^7)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, -1, 0, 1}, {1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, 3, 2, 4}, 70] (* Harvey P. Dale, Nov 06 2017 *)

PROG

(PARI) a(n) = (n^2 + 15*n + 7*(n+8)*(-1)^n + 119)\168 \\ Hoang Xuan Thanh, Aug 29 2025

CROSSREFS

Sequence in context: A029414 A053275 A025816 * A161231 A161055 A161259

Adjacent sequences: A025810 A025811 A025812 * A025814 A025815 A025816

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved