A025811 Expansion of 1/((1-x^2)*(1-x^5)*(1-x^11)).

1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 26

Offset

0,11

Comments

a(n) is the number of partitions of n into parts 2, 5, and 11. - Joerg Arndt, Aug 29 2025

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((n^2 + 18*n + 176)/220 - (n mod 2)/4 + [(n mod 5) in {0,2}]/5). - Hoang Xuan Thanh, Aug 29 2025

a(n) = floor((9*n^2+30*n+44)/44) - floor((n^2+3*n+2)/5)

= floor((11*n^2+18*n+20)/20) - floor((6*n^2+9*n+7)/11)

= (n^2+18*n-8)/220 - (n mod 2)/4 + ((n^2+3*n+2) mod 5)/5 + ((6*n^2+9*n+7) mod 11)/11. - Hoang Xuan Thanh, Oct 08 2025

Prog

(PARI) a(n) = (n^2 + 18*n + 176 - 55*(n%2) + 44*((n%5==0)+(n%5==2)))\220 \\ Hoang Xuan Thanh, Aug 29 2025

Crossrefs

Sequence in context: A105564 A241766 A351646 * A034258 A184349 A290573

Adjacent sequences: A025808 A025809 A025810 * A025812 A025813 A025814

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved