A025824 Expansion of 1/((1-x^2)*(1-x^9)*(1-x^11)).

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

Offset

0,12

Comments

a(n) is the number of partitions of n into parts 2, 9, and 11. - Joerg Arndt, Sep 03 2025

Links

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

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

Formula

a(n) = floor((n^2+22*n+336)/396 - (n mod 2)/4 - (2/3)*[(n mod 9) in {0,5,7}] + (9/11)*[(n mod 11)=0] + (4/11)*([(n mod 11) in {2,9}] - [(n mod 11) in {1,3,8,10}])). - Hoang Xuan Thanh, Sep 03 2025

Prog

(PARI) a(n) = (n^2 + 22*n + 396)/396 - (n%2)/4 + [0, 5, 3, 3, 5, 0, 6, -4, 6][n%9+1]/9 - [0, 15, 5, 14, 9, 12, 12, 9, 14, 5, 15][n%11+1]/11 \\ Hoang Xuan Thanh, Sep 03 2025

Crossrefs

Sequence in context: A268173 A008617 A339369 * A230037 A211262 A185319

Adjacent sequences: A025821 A025822 A025823 * A025825 A025826 A025827

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved