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Expansion of 1 / ((1-x-x^2-x^3)*(1-x^2-x^3)).
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%I #5 May 03 2017 08:42:13

%S 1,1,3,6,11,22,41,77,144,267,495,915,1689,3115,5740,10572,19464,35825,

%T 65926,121301,223166,410544,755211,1389186,2555292,4700154,8645248,

%U 15901510,29247993,53796183,98947583,181994272,334741367,615687632

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

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

%H G. C. Greubel, <a href="/A103322/b103322.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,1,-2,-2,-1).

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

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

%F 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

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

%o (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

%K nonn

%O 0,3

%A _Ralf Stephan_, Feb 02 2005