A025836 Expansion of 1/((1-x^3)(1-x^5)(1-x^8)).

1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 2, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 4, 5, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 14, 13, 14, 15, 14, 16, 16, 16, 18, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23

Offset

0,9

Comments

Partitions of n into parts 3, 5 and 8. - David Neil McGrath, Sep 03 2014

Links

Table of n, a(n) for n=0..67.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -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)=1, a(7)=0, a(8)=2, a(9)=1, a(10)=1, a(11)=2, a(12)=1, a(13)=2, a(14)=2, a(15)=2, a(n)=a(n-3)+ a(n-5)-a(n-11)-a(n-13)+a(n-16). - Harvey P. Dale, Jan 18 2014

a(n) = floor((1/240)*n^2+(1/15)*n+3/4+(1/27)*cos((1/4)*n*Pi)+(1/5)*cos((3/4)*n*Pi)+(1/5)*cos((5/4)*n*Pi)+(1/27)*cos((7/4)*n*Pi)-(1/31)*sin((2/5)*n*Pi)+(1/7)*sin((4/5)*n*Pi)-(1/7)*sin((6/5)*n*Pi)+(1/31)*sin((8/5)*n*Pi)+(1/22)*cos((2/5)*n*Pi)-(1/22)*cos((4/5)*n*Pi)-(1/22)*cos((6/5)*n*Pi)+(1/22)*cos((8/5)*n*Pi)). - Robert Israel, Sep 03 2014

Maple

f:= LREtools[REtoproc](a(n)=a(n-3)+ a(n-5)-a(n-11)-a(n-13)+a(n-16), a(n), {a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=1, a(6)=1, a(7)=0, a(8)=2, a(9)=1, a(10)=1, a(11)=2, a(12)=1, a(13)=2, a(14)=2, a(15)=2}):
seq(f(n), n=0..100); # Robert Israel, Sep 03 2014

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^8)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1}, {1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 2, 1, 2, 2, 2}, 70] (* Harvey P. Dale, Jan 18 2014 *)

Crossrefs

Sequence in context: A029311 A217869 A116674 * A029319 A243987 A050205

Adjacent sequences: A025833 A025834 A025835 * A025837 A025838 A025839

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved