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%I #16 Feb 24 2021 02:48:18
%S 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 94,98,106,114,122,130,146,162,164,166,170,174,178,182,190,198,202,
%U 206,214,222,230,238,254,270,274,278,286,294,302,310,326,342,350,358,374,390,406
%N Leftist toothpicks (see Comments for definition).
%C Similar to A139250, except that when we add toothpicks to horizontal toothpicks, we only add them at the left-hand end.
%C Sequence gives total number of toothpicks in the n-th generation. First differences are in A060632.
%C 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 Seiichi Manyama, <a href="/A151566/b151566.txt">Table of n, a(n) for n = 0..10000</a>
%H 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 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 a(2n) = 2*A006046(n), a(2n+1) = a(2n) + A001316(n) = 2*A006046(n) + A001316(n).
%F G.f.: (x*(1+x)/(1-x)) * Product_{k>0} (1 + 2 * x^(2^k)). - _Seiichi Manyama_, Oct 12 2019
%Y Cf. A001316, A006046.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 23 2009
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