A103322 Expansion of 1 / ((1-x-x^2-x^3)*(1-x^2-x^3)).

1, 1, 3, 6, 11, 22, 41, 77, 144, 267, 495, 915, 1689, 3115, 5740, 10572, 19464, 35825, 65926, 121301, 223166, 410544, 755211, 1389186, 2555292, 4700154, 8645248, 15901510, 29247993, 53796183, 98947583, 181994272, 334741367, 615687632

Offset

0,3

References

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 47, ex. 4.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = A000073(n+3) - A000930(n+4).

a(n) = Sum_{k=0..n} A000073(k+2)*A000930(n-k+3).

a(n) = a(n-1) + 2*a(n-2) +a(n-3) - 2*a(n-4) - 2*a(n-5) - a(n-6). - G. C. Greubel, May 02 2017

Mathematica

CoefficientList[Series[1/((1 - x - x^2 - x^3)*(1 - x^2 - x^3)), {x, 0, 50}], x] (* G. C. Greubel, May 02 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(1/((1 - x - x^2 - x^3)*(1 - x^2 - x^3))) \\ G. C. Greubel, May 02 2017

Crossrefs

Sequence in context: A228206 A195734 A018177 * A284474 A117075 A024506

Adjacent sequences: A103319 A103320 A103321 * A103323 A103324 A103325

Keyword

nonn

Author

Ralf Stephan, Feb 02 2005

Status

approved