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A161210 Toothpick sequence starting at the outside corner of an infinite cube from which protrudes a half toothpick.

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%I A161210 #10 Jun 14 2022 14:12:00
%S A161210 0,1,3,7,14,21,28
%N A161210 Toothpick sequence starting at the outside corner of an infinite cube from which protrudes a half toothpick.
%C A161210 The sequence gives the number of toothpicks after n rounds. A161211 (the first differences) gives the number added at the n-th round.
%C A161210 This structure is a three-dimensional version of the toothpick structure of A153006.
%C A161210 Toothpicks are placed following a rotation of axes: x,y,z,x,y,z,... and so on.
%C A161210 See A139250 and A160160 for more information about the toothpick sequences.
%H A161210 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 A161210 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>
%Y A161210 Cf. A139250, A152980, A153006, A160160, A161211, A161212, A161214, A161216.
%K A161210 more,nonn
%O A161210 0,3
%A A161210 _Omar E. Pol_, Jun 06 2009