A025848 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^11)).

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

Offset

0,15

Comments

Number of partitions of n into parts 3, 7, and 11. - Hoang Xuan Thanh, Sep 06 2025

Links

Table of n, a(n) for n=0..72.

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

Formula

a(n) = floor((n^2 + 21*n + 135)/462 + (5/42)*(((n+2) mod 3) - (n mod 3)) + ((2*n^2 + 6) mod 7)/7). - Hoang Xuan Thanh, Sep 06 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^11)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2}, 80] (* Harvey P. Dale, Aug 28 2017 *)

Prog

(PARI) a(n)= (n^2 + 21*n + 135 + 55*((n+2)%3-n%3) + 66*((2*n^2+6)%7)) \462 \\ Hoang Xuan Thanh, Sep 06 2025

Crossrefs

Sequence in context: A278341 A276520 A242062 * A268197 A065382 A066888

Adjacent sequences: A025845 A025846 A025847 * A025849 A025850 A025851

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved