A025822 Expansion of 1/((1-x^2)*(1-x^8)*(1-x^11)).

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

Offset

0,9

Comments

Number of partitions of n into parts 2, 8, and 11. - Hoang Xuan Thanh, Sep 02 2025

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = floor((n^2 + 21*n + 242)/352 + ((n+10)*(-1)^n + ((n+7) mod 8) + ((n+4) mod 8) - ((n+5) mod 8) - (n mod 8))/32). - Hoang Xuan Thanh, Sep 02 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^8)(1-x^11)), {x, 0, 80}], x] (* or *) LinearRecurrence[ {0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1}, {1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 2, 1, 3, 1, 3, 2, 3}, 80] (* Harvey P. Dale, Jan 05 2023 *)

Prog

(PARI)
up_to = 10000;
A025822list(up_to_n) = { default(seriesprecision, 2+up_to_n); my(s=Ser(1/((1-x^2)*(1-x^8)*(1-x^11))), v=vector(1+up_to_n)); for(n=1, #v, v[n] = polcoeff(s, n-1)); (v); };
v025822 = A025822list(up_to);
A025822(n) = v025822[1+n]; \\ Antti Karttunen, Nov 27 2024
(PARI) a(n) = (n^2+21*n+220 + 11*(n+10)*(-1)^n + 88*((n%8==0)+(n%8==3))) \352 \\ Hoang Xuan Thanh, Sep 02 2025

Crossrefs

Sequence in context: A306439 A107455 A039701 * A051585 A049115 A294204

Adjacent sequences: A025819 A025820 A025821 * A025823 A025824 A025825

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved