A029416 Expansion of 1/((1-x^6)(1-x^7)(1-x^8)(1-x^12)).

1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 2, 1, 1, 0, 2, 2, 3, 2, 2, 1, 4, 2, 4, 3, 4, 2, 5, 4, 6, 4, 5, 4, 8, 5, 8, 6, 8, 5, 10, 8, 11, 8, 10, 8, 14, 10, 14, 11, 14, 10, 17, 14, 19, 14, 17, 14, 22, 17, 23, 19, 23, 17, 26, 22, 29

Offset

0,13

Links

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

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

Formula

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

Mathematica

CoefficientList[Series[1/((1-x^6)(1-x^7)(1-x^8)(1-x^12)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, -1, -1, -1, 0, 0, -1, -1, -1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 2, 1, 1, 0, 2, 2, 3, 2, 2, 1, 4, 2, 4, 3, 4, 2, 5, 4, 6}, 70] (* Harvey P. Dale, Apr 13 2015 *)

Prog

(PARI) Vec(1/((1-x^6)*(1-x^7)*(1-x^8)*(1-x^12))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Crossrefs

Sequence in context: A287160 A029443 A078508 * A252374 A344569 A341094

Adjacent sequences: A029413 A029414 A029415 * A029417 A029418 A029419

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved