A025800 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^11)).

1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 21, 21, 22, 23, 24, 24, 26, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38

Offset

0,7

Comments

Number of partitions of n into parts 2, 3, and 11. - Hoang Xuan Thanh, Aug 26 2025

Links

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

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

Formula

a(n) = floor((n^2 + 16*(n+(-1)^n) + 116)/132 - (n mod 3)*(2 - (n mod 3))/3). - Hoang Xuan Thanh, Aug 26 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^11)), {x, 0, 90}], x] (* Harvey P. Dale, Jun 04 2017 *)
(* Alternative: *)
LinearRecurrence[{0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 1}, {1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 3, 3, 4, 4}, 90] (* Harvey P. Dale, Jun 04 2017 *)

Prog

(PARI) a(n) = (n^2 +16*n +132 -33*(n%2) +44*(n%3)*(n%3-2))\132 \\ Hoang Xuan Thanh, Aug 26 2025

Crossrefs

Sequence in context: A385970 A232194 A054705 * A029258 A280128 A367055

Adjacent sequences: A025797 A025798 A025799 * A025801 A025802 A025803

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved