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A182841 Number of toothpicks added at n-th stage in the toothpick structure of A182840.

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