A029026 Expansion of 1/((1-x)(1-x^2)(1-x^8)(1-x^11)).

1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 12, 14, 15, 18, 19, 22, 24, 27, 29, 33, 35, 40, 42, 47, 50, 55, 58, 64, 67, 74, 78, 85, 90, 97, 102, 110, 115, 124, 130, 139, 146, 156, 163, 174, 181, 193, 201, 213, 222, 235, 244

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 8 and 11. - Ilya Gutkovskiy, May 14 2017

Links

Table of n, a(n) for n=0..53.

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 2, -1, -1, 1, 0, 0, 0, 0, -1, 1, 1, -1).

Formula

a(0)=1, a(1)=1, a(2)=2, a(3)=2, a(4)=3, a(5)=3, a(6)=4, a(7)=4, a(8)=6, a(9)=6, a(10)=8, a(11)=9, a(12)=11, a(13)=12, a(14)=14, a(15)=15, a(16)=18, a(17)=19, a(18)=22, a(19)=24, a(20)=27, a(21)=29, a(n)= a(n-1)+ a(n-2)-a(n-3)+a(n-8)-a(n-9)-a(n-10)+2*a(n-11)- a(n-12)-a(n-13)+ a(n-14)-a(n-19)+a(n-20)+a(n-21)-a(n-22). - Harvey P. Dale, Nov 02 2015

Maple

M:= Matrix(22, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 2, -1, -1, 1, 0, 0, 0, 0, -1, 1, 1, -1][i] else 0 fi); a:= n-> (M^(n))[1, 1]; seq(a(n), n=0..53); # Alois P. Heinz, Jul 31 2008

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^8)(1-x^11)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 2, -1, -1, 1, 0, 0, 0, 0, -1, 1, 1, -1}, {1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 12, 14, 15, 18, 19, 22, 24, 27, 29}, 60] (* Harvey P. Dale, Nov 02 2015 *)

Crossrefs

Sequence in context: A362612 A319169 A050365 * A003106 A185228 A026824

Adjacent sequences: A029023 A029024 A029025 * A029027 A029028 A029029

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved