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 A151566 #16 Feb 24 2021 02:48:18
%S A151566 0,1,2,4,6,8,10,14,18,20,22,26,30,34,38,46,54,56,58,62,66,70,74,82,90,
%T A151566 94,98,106,114,122,130,146,162,164,166,170,174,178,182,190,198,202,
%U A151566 206,214,222,230,238,254,270,274,278,286,294,302,310,326,342,350,358,374,390,406
%N A151566 Leftist toothpicks (see Comments for definition).
%C A151566 Similar to A139250, except that when we add toothpicks to horizontal toothpicks, we only add them at the left-hand end.
%C A151566 Sequence gives total number of toothpicks in the n-th generation. First differences are in A060632.
%C A151566 This is equivalent to the Sierpinski triangle A047999. Each inverted T formed by two toothpicks is equivalent to a triangle in the Sierpinski sieve. See Gould's sequence A001316. [From _Omar E. Pol_, May 23 2009]
%H A151566 Seiichi Manyama, <a href="/A151566/b151566.txt">Table of n, a(n) for n = 0..10000</a>
%H A151566 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H A151566 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%F A151566 a(2n) = 2*A006046(n), a(2n+1) = a(2n) + A001316(n) = 2*A006046(n) + A001316(n).
%F A151566 G.f.: (x*(1+x)/(1-x)) * Product_{k>0} (1 + 2 * x^(2^k)). - _Seiichi Manyama_, Oct 12 2019
%Y A151566 Cf. A001316, A006046.
%K A151566 nonn,easy
%O A151566 0,3
%A A151566 _N. J. A. Sloane_, May 23 2009