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 A100138 #15 Oct 10 2021 22:59:24
%S A100138 1,2,4,8,16,32,66,144,336,832,2144,5632,14852,38968,101312,260736,
%T A100138 664704,1681152,4226056,10578080,26407648,65838848,164095360,
%U A100138 409129472,1020795408,2549137824,6371133120,15935185792,39878810624,99837958144
%N A100138 a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-5k).
%C A100138 Binomial transform of 1,1,1,1,1,1,3,3,9,9,21,... with g.f. (1-x)^2(1+x)^2/(1-3x^2+3x^4-3x^6)=(1+x)(1-x^2)^2/((1-x^2)^3-2x^6).
%H A100138 Seiichi Manyama, <a href="/A100138/b100138.txt">Table of n, a(n) for n = 0..1000</a>
%H A100138 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8,0,0,2).
%F A100138 G.f.: (1-2x)^2/((1-2x)^3 - 2x^6).
%F A100138 a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) + 2*a(n-6).
%t A100138 Table[Sum[Binomial[n-3k,3k]2^(n-5k),{k,0,Floor[n/6]}],{n,0,30}] (* or *) LinearRecurrence[{6,-12,8,0,0,2},{1,2,4,8,16,32},30] (* _Harvey P. Dale_, Dec 30 2019 *)
%Y A100138 Cf. A052101, A100132, A100134, A100137, A100139.
%K A100138 easy,nonn
%O A100138 0,2
%A A100138 _Paul Barry_, Nov 06 2004