This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080925 #15 Aug 27 2025 07:00:05
%S A080925 0,1,5,13,41,121,365,1093,3281,9841,29525,88573,265721,797161,2391485,
%T A080925 7174453,21523361,64570081,193710245,581130733,1743392201,5230176601,
%U A080925 15690529805,47071589413,141214768241,423644304721,1270932914165
%N A080925 Binomial transform of Jacobsthal gap sequence (A080924).
%H A080925 Vincenzo Librandi, <a href="/A080925/b080925.txt">Table of n, a(n) for n = 0..300</a>
%H A080925 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).
%F A080925 a(n)=Sum{k=1..n, Binomial(n, 2k-2)2^(2k-2)}
%F A080925 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 A080925 CoefficientList[Series[x (1 + 3 x) / ((1 + x) (1 - 3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%Y A080925 Cf. A080926. Essentially the same as A046717.
%K A080925 easy,nonn,changed
%O A080925 0,3
%A A080925 _Paul Barry_, Feb 26 2003