A029110 Expansion of 1/((1-x)(1-x^6)(1-x^7)(1-x^12)).

1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 5, 6, 7, 7, 7, 7, 9, 11, 12, 13, 13, 13, 16, 18, 20, 21, 22, 22, 25, 28, 30, 32, 33, 34, 38, 41, 44, 46, 48, 49, 54, 58, 61, 64, 66, 68, 74, 79, 83, 86, 89, 91, 98, 104, 109, 113, 116, 119

Offset

0,7

Links

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

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

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=2, a(7)=3, a(8)=3, a(9)=3, a(10)=3, a(11)=3, a(12)=5, a(13)=6, a(14)=7, a(15)=7, a(16)=7, a(17)=7, a(18)=9, a(19)=11, a(20)=12, a(21)=13, a(22)=13, a(23)=13, a(24)=16, a(25)=18, a(n)=a(n-1)+a(n-6)-a(n-8)+a(n-12)-2*a(n-13)+ a(n-14)- a(n-18)+a(n-20)+a(n-25)-a(n-26). - Harvey P. Dale, May 25 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-x^6)(1-x^7)(1-x^12)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 5, 6, 7, 7, 7, 7, 9, 11, 12, 13, 13, 13, 16, 18}, 80] (* Harvey P. Dale, May 25 2013 *)

Crossrefs

Sequence in context: A280455 A284725 A055767 * A249420 A103959 A035375

Adjacent sequences: A029107 A029108 A029109 * A029111 A029112 A029113

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved