%I
%S 0,1,5,13,41,121,365,1093,3281,9841,29525,88573,265721,797161,2391485,
%T 7174453,21523361,64570081,193710245,581130733,1743392201,5230176601,
%U 15690529805,47071589413,141214768241,423644304721,1270932914165
%N Binomial transform of Jacobsthal gap sequence (A080924).
%H Vincenzo Librandi, <a href="/A080925/b080925.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,3).
%F a(n)=Sum{k=1..n, Binomial(n, 2k2)2^(2k2)}
%F a(n)=(3^n2*0^n+(1)^n)/2; G.f.: x(1+3x)/((1+x)(13x)); E.g.f.: (exp(3x)2exp(0)+exp(x))/2.  _Paul Barry_, May 19 2003
%t CoefficientList[Series[x (1 + 3 x) / ((1 + x) (1  3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%Y Cf. A046717, A080926.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Feb 26 2003
