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%I #6 Jun 13 2015 00:51:34
%S 0,0,1,6,25,88,281,842,2413,6692,18101,48014,125393,323376,825393,
%T 2088850,5248853,13110844,32584653,80639446,198844281,488813768,
%U 1198491913,2931934938,7158830781,17450923092,42480107365,103283553054
%N Sum C(n-k,k+2)2^(n-k-2)(1/2)^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,-11,4,4).
%F G.f.: x^2/((1-2x)^2(1-2x-x^2)); a(n)=sum{k=0..floor(n/2), C(n-k, k+2)2^(n-2k-2)}; a(n)=6a(n-1)-11a(n-2)+4a(n-3)+4a(n-4).
%Y Cf. A099623, A099624.
%K easy,nonn
%O 0,4
%A _Paul Barry_, Oct 25 2004
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