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 A116413 #16 Aug 06 2024 02:14:34
%S A116413 1,3,7,18,46,117,298,759,1933,4923,12538,31932,81325,207120,527497,
%T A116413 1343439,3421495,8713926,22192786,56520993,143948698,366611175,
%U A116413 933692041,2377943955,6056191126,15424018248,39282171577,100044552528,254795294881,648917313867
%N A116413 Expansion of (1+x)/(1-2x-x^2-x^3).
%C A116413 Diagonal sums of number triangle A116412. A078058 is an alternating sign version.
%C A116413 4*a(n) is the number of ways to tile a strip of length n+2 with red and blue squares, blue dominos, and blue trominos, where the first two tiles must have total length <= 3. - _Greg Dresden_ and Arnim Kuchhal, Aug 05 2024
%H A116413 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,1).
%F A116413 a(n) = 2a(n-1)+a(n-2)+a(n-3).
%F A116413 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} C(k+1,j)*C(n-k-j,k)*2^(n-2k-j).
%t A116413 CoefficientList[Series[(1+x)/(1-2x-x^2-x^3),{x,0,50}],x] (* or *) LinearRecurrence[{2,1,1},{1,3,7},50] (* _Vladimir Joseph Stephan Orlovsky_, Jan 31 2012 *)
%K A116413 easy,nonn
%O A116413 0,2
%A A116413 _Paul Barry_, Feb 13 2006