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 A113726 #20 Apr 30 2025 15:35:40
%S A113726 1,0,1,4,5,8,25,44,77,176,353,660,1365,2776,5417,10876,21981,43648,
%T A113726 87153,175076,349669,698280,1398585,2797260,5590381,11184720,22373761,
%U A113726 44735284,89474165,178969208,357910345,715807004,1431683837,2863325216
%N A113726 A Jacobsthal convolution.
%C A113726 Convolution of A001045(n+1) and A001607(n+1).
%H A113726 Harvey P. Dale, <a href="/A113726/b113726.txt">Table of n, a(n) for n = 0..1000</a>
%H A113726 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,4,4).
%F A113726 G.f.: 1/((1-x-2*x^2)*(1+x+2*x^2)).
%F A113726 a(n) = a(n-2) + 4*a(n-3) + 4*a(n-4).
%F A113726 a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*2^k*(1+(-1)^(n-k))/2.
%F A113726 a(n) = 2^n/3 + (-1)^n/6 + A001607(n+1)/2. - _R. J. Mathar_, Aug 23 2011
%F A113726 a(n) = sum(A128099(n, n-2*k), k=0..floor(n/2)). - _Johannes W. Meijer_, Aug 28 2013
%t A113726 LinearRecurrence[{0,1,4,4},{1,0,1,4},40] (* _Harvey P. Dale_, Apr 30 2025 *)
%Y A113726 Cf. A094686, A089977, A001045, A001607.
%K A113726 easy,nonn
%O A113726 0,4
%A A113726 _Paul Barry_, Nov 08 2005