A025806 Expansion of 1/((1-x^2)*(1-x^5)*(1-x^6)).

1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 3, 2, 4, 2, 4, 3, 5, 4, 6, 4, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 13, 10, 14, 11, 15, 13, 17, 14, 18, 15, 20, 17, 22, 18, 23, 20, 25, 22, 27, 23, 29, 25, 31, 27, 33, 29, 35, 31, 37, 33, 40, 35, 42, 37

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 5, and 6. - Joerg Arndt, May 24 2025

Links

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

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

Formula

G.f.: 1/((1-x^2)*(1-x^5)*(1-x^6)).

a(n) = a(n-2) + a(n-5) + a(n-6) - a(n-7) - a(n-8) - a(n-11) + a(n-13). - Wesley Ivan Hurt, Apr 18 2023

a(n) = floor((n^2+n*(13+5*(-1)^n)+90+30*(-1)^n)/120). - Hoang Xuan Thanh, May 23 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^5)(1-x^6)), {x, 0, 90}], x] (* Harvey P. Dale, May 06 2022 *)

Crossrefs

Sequence in context: A217317 A331128 A154958 * A025802 A145706 A139631

Adjacent sequences: A025803 A025804 A025805 * A025807 A025808 A025809

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved