A029194 Expansion of 1/((1-x^2)*(1-x^5)*(1-x^6)*(1-x^8)).

1, 0, 1, 0, 1, 1, 2, 1, 3, 1, 4, 2, 5, 3, 6, 4, 8, 5, 10, 6, 12, 8, 14, 10, 17, 12, 20, 14, 23, 17, 27, 20, 31, 23, 35, 27, 40, 31, 45, 35, 51, 40, 57, 45, 63, 51, 70, 57, 78, 63, 86, 70, 94, 78, 103, 86, 113, 94, 123, 103

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is the number of partitions of n into parts 2, 5, 6, and 8. - Joerg Arndt, Jun 11 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,1,1,-1,0,0,-1,-1,0,0,-1,1,1,0,0,1,0,-1).

Crossrefs

Cf. A029032.

Programs

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^5) (1 - x^6) (1 - x^8)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 02 2014 *)
LinearRecurrence[{0,1,0,0,1,1,-1,0,0,-1,-1,0,0,-1,1,1,0,0,1,0,-1},{1,0,1,0,1,1,2,1,3,1,4,2,5,3,6,4,8,5,10,6,12},100] (* Harvey P. Dale, May 28 2017 *)

Formula

From Hoang Xuan Thanh, Jun 11 2025: (Start)

a(2*n) = A029032(n); a(2*n+1) = A029032(n-2) for n > 1.

a(n) = floor((2*n^3 + (63+15*(-1)^n)*n^2 + (597+315*(-1)^n)*n + 4330 + 1430*(-1)^n)/5760). (End)