A025915 Expansion of 1/((1-x^7)*(1-x^10)*(1-x^11)).

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5

Offset

0,22

Comments

Number of partitions of n into parts 7, 10, and 11. - Hoang Xuan Thanh, Sep 26 2025

Links

Table of n, a(n) for n=0..79.

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

Formula

a(n) = floor((7*n^2+9*n+2)/11) - floor((2*n^2+6)/7) + floor((-7*n^2-16*n+23)/20). - Hoang Xuan Thanh, Sep 26 2025

Mathematica

CoefficientList[Series[1/((1-x^7)(1-x^10)(1-x^11)), {x, 0, 100}], x] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 1}, 100] (* Harvey P. Dale, Aug 06 2023 *)

Prog

(PARI) a(n) = (n^2+28*n-809)/1540 + ((2*n^2+6)%7)/7 - ((7*n^2+9*n+2)%11)/11 + ((7*n^2+16*n+17)%20)/20 + (n%10==1) \\ Hoang Xuan Thanh, Sep 26 2025

Crossrefs

Sequence in context: A299908 A044933 A295343 * A081285 A255361 A341685

Adjacent sequences: A025912 A025913 A025914 * A025916 A025917 A025918

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved