A025842 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^8)).

1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 3, 0, 2, 3, 1, 2, 4, 1, 3, 4, 2, 3, 6, 2, 4, 6, 3, 4, 8, 3, 6, 8, 4, 6, 10, 4, 8, 10, 6, 8, 12, 6, 10, 12, 8, 10, 15, 8, 12, 15, 10, 12, 18, 10, 15, 18, 12, 15, 21, 12, 18, 21, 15, 18, 24, 15, 21

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Comments

a(n) is the number of partitions of n into parts 3, 6, and 8. - Michel Marcus, Jun 30 2025

Links

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

Crossrefs

Cf. A001972, A004526.

Programs

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^8)),{x,0,70}],x] (* Harvey P. Dale, Jan 25 2012 *)

Formula

a(3*n) = a(3*n+8) = a(3*n+16) = A001972(A004526(n)). - Hoang Xuan Thanh, Jun 25 2025

a(n) = floor((n^2+n+124+3*n*(-1)^n)/288 + (n+6)*((n+2) mod 3)/18 + (((n+1) mod 6) - (n mod 6))/36). - Hoang Xuan Thanh, Sep 04 2025