A029187 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^8)*(1-x^11)).

1, 0, 1, 0, 2, 0, 2, 0, 4, 0, 4, 1, 6, 1, 6, 2, 9, 2, 9, 4, 12, 4, 13, 6, 17, 6, 18, 9, 22, 9, 24, 12, 29, 13, 31, 17, 36, 18, 39, 22, 45, 24, 48, 29, 55, 31, 59, 36, 67, 39, 71, 45, 80, 48, 85, 55, 95, 59, 100, 67, 111, 71, 117

Offset

0,5

Comments

a(n) is the number of partitions of n into parts 2, 4, 8, and 11. - Hoang Xuan Thanh, Oct 11 2025

Links

Table of n, a(n) for n=0..62.

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

Formula

a(n) = floor((n^3+54*n^2+764*n+4824)/4224 - (n^2+25*n+120)*(n mod 2)/128 + (n+10)*((n^2+n+2) mod 4)/64). - Hoang Xuan Thanh, Oct 11 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^8)(1-x^11)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 1, -1, -1, 1, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1}, {1, 0, 1, 0, 2, 0, 2, 0, 4, 0, 4, 1, 6, 1, 6, 2, 9, 2, 9, 4, 12, 4, 13, 6, 17}, 80] (* Harvey P. Dale, Jul 13 2015 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^8)*(1-x^11)) + O(x^70)) \\ Hoang Xuan Thanh, Oct 11 2025

Crossrefs

Sequence in context: A132952 A319998 A336120 * A201863 A035385 A051629

Adjacent sequences: A029184 A029185 A029186 * A029188 A029189 A029190

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved