A029368 Expansion of 1/((1-x^4)(1-x^7)(1-x^11)(1-x^12)).

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 2, 0, 2, 3, 2, 1, 3, 4, 3, 2, 4, 4, 4, 3, 5, 5, 5, 5, 6, 7, 7, 6, 7, 8, 9, 7, 9, 10, 11, 9, 11, 13, 13, 11, 13, 15, 15, 13, 16, 18, 18, 16, 19, 21, 21, 19, 22, 24, 24, 22, 26, 28, 28

Offset

0,12

Links

Table of n, a(n) for n=0..68.

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

Formula

G.f.: 1/((1-x^4)(1-x^7)(1-x^11)(1-x^12)).

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=0, a(6)=0, a(7)=1, a(8)=1, a(9)=0, a(10)=0, a(11)=2, a(12)=2, a(13)=0, a(14)=1, a(15)=2, a(16)=2, a(17)=0, a(18)=2, a(19)=3, a(20)=2, a(21)=1, a(22)=3, a(23)=4, a(24)=3, a(25)=2, a(26)=4, a(27)=4, a(28)=4, a(29)=3, a(30)=5, a(31)=5, a(32)=5, a(33)=5, a(n)= a(n-4)+a(n-7)+a(n-12)-a(n-15)-a(n-16)-a(n-18)-a(n-19)+a(n-22)+ a(n-27)+ a(n-30)- a(n-34). - Harvey P. Dale, Jun 03 2015

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^11)(1-x^12)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 2, 0, 2, 3, 2, 1, 3, 4, 3, 2, 4, 4, 4, 3, 5, 5, 5, 5}, 100] (* Harvey P. Dale, Jun 03 2015 *)

Crossrefs

Sequence in context: A256171 A058643 A343748 * A108483 A363623 A101565

Adjacent sequences: A029365 A029366 A029367 * A029369 A029370 A029371

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved