A103321 Expansion of 1 / ((1-x-x^2-x^3)*(1-x-x^3)).

1, 2, 4, 9, 18, 35, 68, 130, 246, 463, 867, 1617, 3007, 5579, 10332, 19107, 35295, 65140, 120137, 221444, 407999, 751453, 1383641, 2547116, 4688106, 8627504, 15875390, 29209560, 53739655, 98864470, 181872110, 334561861, 615423932

Offset

0,2

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

Antonín Slavík and Marie Vestenická, Through the Tiling Glass: Tribonacci Identities, Univ. Karlova (Czechia, 2026). See p. 12.

Index entries for linear recurrences with constant coefficients, signature (2,0,1,-2,-1,-1).

Formula

a(n) = A000073(n+4) - A000930(n+2).

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

a(0)=1, a(1)=2, a(2)=4, a(3)=9, a(4)=18, a(5)=35, a(n)=2*a(n-1)+a(n-3)- 2*a(n-4)-a(n-5)-a(n-6). - Harvey P. Dale, Nov 06 2011

Mathematica

CoefficientList[Series[1/((1-x-x^2-x^3)(1-x-x^3)), {x, 0, 40}], x] (* Harvey P. Dale, Nov 06 2011 *)
(* Alternative: *)
LinearRecurrence[{2, 0, 1, -2, -1, -1}, {1, 2, 4, 9, 18, 35}, 40] (* Harvey P. Dale, Nov 06 2011 *)

Prog

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

Crossrefs

Sequence in context: A065055 A065030 A395396 * A138196 A298404 A101351

Adjacent sequences: A103318 A103319 A103320 * A103322 A103323 A103324

Keyword

nonn,easy

Author

Ralf Stephan, Feb 02 2005

Status

approved