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 A080925 Binomial transform of Jacobsthal gap sequence (A080924). 6

%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 entries for linear recurrences with constant coefficients</a>, signature (2,3).

%F a(n)=Sum{k=1..n, Binomial(n, 2k-2)2^(2k-2)}

%F a(n)=(3^n-2*0^n+(-1)^n)/2; G.f.: x(1+3x)/((1+x)(1-3x)); 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

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