A083707 G.f.: (x+4*x^3+x^5)/((1-x)^2*(1-x^2)^2*(1-x^3)).

0, 1, 2, 9, 17, 37, 63, 108, 165, 252, 358, 506, 684, 917, 1192, 1539, 1941, 2433, 2997, 3670, 4433, 5328, 6332, 7492, 8784, 10257, 11886, 13725, 15745, 18005, 20475, 23216, 26197, 29484, 33042, 36942, 41148, 45733, 50660, 56007, 61733, 67921, 74529, 81642

Offset

0,3

References

H. Gupta, Magic partitions, I, Math. Student 45 (1977), no. 3, 58-62.

Links

Table of n, a(n) for n=0..43.

Index entries for linear recurrences with constant coefficients, signature (2, 1, -3, -1, 1, 3, -1, -2, 1).

Formula

a(0)=0, a(1)=1, a(2)=2, a(3)=9, a(4)=17, a(5)=37, a(6)=63, a(7)=108, a(8)=165, a(n)=2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)- a(n-7)-2*a(n-8)+ a(n-9). - Harvey P. Dale, May 01 2015

Mathematica

CoefficientList[Series[(x+4x^3+x^5)/((1-x)^2(1-x^2)^2(1-x^3)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {0, 1, 2, 9, 17, 37, 63, 108, 165}, 50] (* Harvey P. Dale, May 01 2015 *)

Crossrefs

Cf. A083708, A083709.

Sequence in context: A028503 A100291 A126082 * A240651 A357432 A369000

Adjacent sequences: A083704 A083705 A083706 * A083708 A083709 A083710

Keyword

nonn

Author

N. J. A. Sloane, Jun 15 2003

Status

approved