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Expansion of (1 - x - x^3)/((1 - x - x^3)^2 - 4*x^4).
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%I #11 Aug 10 2024 11:04:08

%S 1,1,1,2,7,16,30,61,137,303,644,1365,2936,6340,13625,29209,62701,

%T 134758,289547,621816,1335378,2868341,6161329,13233947,28424456,

%U 61052489,131135696,281667368,604991601,1299458257,2791106585,5995020362,12876698159,27657838272

%N Expansion of (1 - x - x^3)/((1 - x - x^3)^2 - 4*x^4).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,2,0,-1).

%F a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-6).

%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-4*k,2*k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec((1-x-x^3)/((1-x-x^3)^2-4*x^4))

%o (PARI) a(n) = sum(k=0, n\3, binomial(2*n-4*k, 2*k));

%Y Cf. A108479, A375278.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Aug 09 2024