A025802 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^5)).

1, 0, 1, 0, 2, 1, 2, 1, 3, 2, 4, 2, 5, 3, 6, 4, 7, 5, 8, 6, 10, 7, 11, 8, 13, 10, 14, 11, 16, 13, 18, 14, 20, 16, 22, 18, 24, 20, 26, 22, 29, 24, 31, 26, 34, 29, 36, 31, 39, 34, 42, 36, 45, 39, 48, 42, 51, 45, 54, 48, 58, 51

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is the number of partitions of n into parts 2, 4, and 5. - Hoang Xuan Thanh, Jun 18 2025

Links

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

Crossrefs

Cf. A000115.

Programs

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^5)),{x,0,70}],x] (* Harvey P. Dale, Sep 15 2011 *)

Formula

From R. J. Mathar, Jun 23 2021: (Start)

a(n)-a(n-2) = A165190(n).

a(n)-a(n-4) = A008616(n). (End)

a(n) = floor((n^2 + n*(11+5*(-1)^n) + 53 + 27*(-1)^n)/80). - Hoang Xuan Thanh, Jun 18 2025