A029190 Expansion of 1/((1-x^2)(1-x^4)(1-x^9)(1-x^12)).

1, 0, 1, 0, 2, 0, 2, 0, 3, 1, 3, 1, 5, 2, 5, 2, 7, 3, 8, 3, 10, 5, 11, 5, 14, 7, 15, 8, 18, 10, 20, 11, 23, 14, 25, 15, 30, 18, 32, 20, 37, 23, 40, 25, 45, 30, 48, 32, 55, 37, 58, 40, 65, 45, 70, 48, 77, 55, 82, 58, 91, 65, 96

Offset

0,5

Links

Table of n, a(n) for n=0..62.

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

Formula

a(0)=1, a(1)=0, a(2)=1, a(3)=0, a(4)=2, a(5)=0, a(6)=2, a(7)=0, a(8)=3, a(9)=1, a(10)=3, a(11)=1, a(12)=5, a(13)=2, a(14)=5, a(15)=2, a(16)=7, a(17)=3, a(18)=8, a(19)=3, a(20)=10, a(21)=5, a(22)=11, a(23)=5, a(24)=14, a(25)=7, a(26)=15, a(n)=a(n-2)+a(n-4)-a(n-6)+a(n-9)-a(n-11)+a(n-12)-a(n-13)-a(n-14)+a(n-15)- a(n-16)+ a(n-18)-a(n-21)+a(n-23)+a(n-25)-a(n-27). - Harvey P. Dale, Mar 03 2014

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^9)(1-x^12)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 0, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, -1, 0, 1, 0, 0, -1, 0, 1, 0, 1, 0, -1}, {1, 0, 1, 0, 2, 0, 2, 0, 3, 1, 3, 1, 5, 2, 5, 2, 7, 3, 8, 3, 10, 5, 11, 5, 14, 7, 15}, 70] (* Harvey P. Dale, Mar 03 2014 *)

Crossrefs

Sequence in context: A319973 A025804 A042961 * A166865 A300575 A029189

Adjacent sequences: A029187 A029188 A029189 * A029191 A029192 A029193

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved