A029015 Expansion of 1/((1-x)(1-x^2)(1-x^5)(1-x^11)).

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 21, 24, 27, 30, 33, 37, 41, 46, 50, 55, 60, 66, 72, 78, 84, 91, 98, 106, 114, 122, 131, 140, 150, 160, 170, 181, 192, 204, 216, 229, 242, 256, 270, 285, 300, 316, 332, 349, 366, 384, 403, 422, 442, 462, 483

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 5 and 11. - Ilya Gutkovskiy, May 14 2017

Links

Table of n, a(n) for n=0..59.

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

Formula

a(0)=1, a(1)=1, a(2)=2, a(3)=2, a(4)=3, a(5)=4, a(6)=5, a(7)=6, a(8)=7, a(9)=8, a(10)=10, a(11)=12, a(12)=14, a(13)=16, a(14)=18, a(15)=21, a(16)=24, a(17)=27, a(18)=30, a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5) - a(n-6) - a(n-7) + a(n-8) + a(n-11) - a(n-12) - a(n-13) + a(n-14) - a(n-16) + a(n-17) + a(n-18) - a(n-19). - Harvey P. Dale, Dec 24 2011

a(n) = floor((2*n^3 + 57*n^2 + 466*n + 1622)/1320 + (-1)^n/16). - Tani Akinari, May 19 2014

Maple

M := Matrix(19, (i, j)-> if (i=j-1) or (j=1 and member(i, [1, 2, 5, 8, 11, 14, 17, 18])) then 1 elif j=1 and member(i, [3, 6, 7, 12, 13, 16, 19]) then -1 else 0 fi); a := n -> (M^(n))[1, 1]; seq (a(n), n=0..51); # Alois P. Heinz, Jul 25 2008

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^5)(1-x^11)), {x, 0, 60}], x] (* Harvey P. Dale, Dec 24 2011 *)

Prog

(PARI) a(n)=floor((2*n^3+57*n^2+466*n+1622)/1320+(-1)^n/16) \\ Tani Akinari, May 19 2014

Crossrefs

Sequence in context: A029016 A290807 A121385 * A000008 A001312 A182086

Adjacent sequences: A029012 A029013 A029014 * A029016 A029017 A029018

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 1999

Status

approved