A025771 Expansion of 1/((1-x)*(1-x^3)*(1-x^11)).

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 82, 84, 86, 89

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is the number of partitions of n into parts 1, 3, and 11. - Joerg Arndt, Aug 20 2025

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,0,0,0,0,0,1,-1,0,-1,1).

Programs

Maple

A025771 := proc(n)
        round(n^2/66 +5*n/22 +68/99 + A099837(n+3)/9) ;
end proc: # R. J. Mathar, Aug 11 2012

Mathematica

A025771[n_] := Quotient[n*(n + 15) + 78, 66];
Array[A025771, 100, 0] (* Paolo Xausa, Aug 20 2025 *)

PARI

Vec(1/((1-x)*(1-x^3)*(1-x^11))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

a(n) = +a(n-1) +a(n-3) -a(n-4) +a(n-11) -a(n-12) -a(n-14) +a(n-15). - R. J. Mathar, Aug 21 2014

a(n) = floor((n^2 + 15*n + 78)/66). - Hoang Xuan Thanh, Aug 18 2025