A025844 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^11)).

1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 3, 0, 1, 3, 0, 2, 4, 0, 2, 4, 1, 3, 5, 1, 3, 5, 2, 4, 6, 2, 4, 7, 3, 5, 8, 3, 5, 9, 4, 6, 10, 4, 7, 11, 5, 8, 12, 5, 9, 13, 6, 10, 14, 7, 11, 15, 8, 12, 16, 9, 13, 17, 10, 14, 19, 11, 15, 20, 12, 16

Offset

0,7

Comments

Number of partitions of n into parts 3, 6, and 11. - Hoang Xuan Thanh, Sep 04 2025

Links

Table of n, a(n) for n=0..71.

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

Formula

a(n) = floor((n^2 - 2*n + 94)/396 + n*((n+2) mod 3)/18 + (5/22)*((n+2) mod 3)^2 + (10*((n+5) mod 6) - 5*((n+3) mod 6) - 5*(n mod 6))/132). - Hoang Xuan Thanh, Sep 04 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^11)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 3, 0, 1, 3, 0, 2, 4, 0}, 100] (* Harvey P. Dale, Sep 06 2025 *)

Prog

(PARI) a(n) = (n^2 +20*n +396 +22*n*[1, -1, 0][n%3+1] +88*[2, -4, -3, 1, -3, -2][n%6+1]) \396 \\ Hoang Xuan Thanh, Sep 04 2025

Crossrefs

Sequence in context: A112605 A111775 A325166 * A394017 A035461 A118508

Adjacent sequences: A025841 A025842 A025843 * A025845 A025846 A025847

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved