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%I #9 Dec 16 2024 05:47:19
%S 0,0,1,6,27,104,369,1242,4039,12828,40077,123758,379011,1153872,
%T 3498025,10572354,31884543,96010436,288788613,867967830,2607282235,
%U 7828953720,23501774241,70536546986,211674885687,635160738924,1905765565309
%N Sum C(n-k,k+2)2^(n-k-2)(3/2)^k, k=0..floor(n/2).
%C In general a(n)=sum{k=0..floor(n/2), C(n-k,k+2)u^(n-k-2)(v/u)^k has g.f. x^2/((1-u*x)^2(1-u*x-v*x^2)) and satisfies the recurrence a(n)=3u*a(n-1)-(3u^2-v)a(n-2)+(u^3-2uv)a(n-3)+u^2^v*a(n-4).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,-4,12).
%F G.f.: x^2/((1-2x)^2(1-2x-3x^2)); a(n)=6a(n-1)-9a(n-2)-4a(n-3)+12a(n-4).
%F a(n) = -(n/3+7/9)*2^n +(-1)^n/36 +3^(n+1)/4 . - _R. J. Mathar_, Dec 16 2024
%t LinearRecurrence[{6,-9,-4,12},{0,0,1,6},30] (* _Harvey P. Dale_, Mar 27 2016 *)
%K easy,nonn
%O 0,4
%A _Paul Barry_, Oct 25 2004