A029272 Expansion of 1/((1-x^3)(1-x^5)(1-x^6)(1-x^7)).

1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 2, 2, 4, 3, 3, 5, 4, 5, 7, 6, 7, 9, 8, 9, 12, 11, 12, 15, 14, 15, 19, 18, 19, 23, 22, 24, 28, 27, 29, 33, 33, 35, 40, 39, 41, 47, 46, 49, 55, 54, 57, 63, 63, 66, 73, 73, 76, 83, 83, 87, 95, 95

Offset

0,7

Comments

Number of partitions of n into parts 3, 5, 6, and 7. - Vincenzo Librandi, Jun 03 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=1, a(6)=2, a(7)=1, a(8)=1, a(9)=2, a(10)=2, a(11)=2, a(12)=4, a(13)=3, a(14)=3, a(15)=5, a(16)=4, a(17)=5, a(18)=7, a(19)=6, a(20)=7, a(n)=a(n-3)+a(n-5)+a(n-6)+a(n-7)-a(n-8)-a(n-9)- a(n-10)- a(n-11)-a(n-12)-a(n-13)+a(n-14)+a(n-15)+a(n-16)+a(n-18)-a(n-21). - Harvey P. Dale, Apr 08 2013

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^6)(1-x^7)), {x, 0, 90}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 2, 2, 4, 3, 3, 5, 4, 5, 7, 6, 7}, 90] (* Harvey P. Dale, Apr 08 2013 *)

Crossrefs

Sequence in context: A066877 A240071 A029255 * A153904 A128762 A126307

Adjacent sequences: A029269 A029270 A029271 * A029273 A029274 A029275

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved