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%I #49 Feb 24 2021 02:48:19
%S 0,1,4,8,14,16,14,24,38,32,14,24,46,64,54,56,86,64,14,24,46,64,62,80,
%T 126,144,86,56,110,168,158,144,198,128,14,24,46,64,62,80,126,144,94,
%U 80,142,224,238,224,286,304,150,56,110,168,182,216,326,408,302,176,262,408,414,360,438,256
%N Number of toothpicks added at n-th stage in the toothpick structure of A182840.
%C First differences of A182840.
%H Olaf Voß, <a href="/A182841/b182841.txt">Table of n, a(n) for n = 0..1000</a>
%H David Applegate, <a href="/A139250/a139250.anim.html">The movie version</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>
%H Olaf Voß, <a href="/wiki/Toothpick_structures_on_hexagonal_net">Toothpick structures on hexagonal net</a>
%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F a(2^k + 1) = 2^(k+2), at least for 0 <= k <= 9. - _Omar E. Pol_, Nov 01 2014
%e From _Omar E. Pol_, Nov 01 2014: (Start)
%e When written as an irregular triangle:
%e 0;
%e 1;
%e 4;
%e 8;
%e 14, 16;
%e 14, 24, 38, 32;
%e 14, 24, 46, 64, 54, 56, 86, 64;
%e 14, 24, 46, 64, 62, 80, 126, 144, 86, 56, 110, 168, 158, 144, 198, 128;
%e 14, 24, 46, 64, 62, 80, 126, 144, 94, 80, 142, 224, 238, 224, 286, 304, 150, 56, 110, 168, 182, 216, 326, 408, 302, 176, 262, 408, 414, 360, 438, 256;
%e ...
%e (End)
%Y Cf. A139250, A139251, A160121, A161207, A182633, A182635, A151724, A182842.
%K nonn,tabf
%O 0,3
%A _Omar E. Pol_, Dec 09 2010
%E More terms from _Olaf Voß_, Dec 24 2010
%E Wiki link added by _Olaf Voß_, Jan 14 2011
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