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Number of Q-toothpicks added at n-th stage to the structure of A187212.
3

%I #17 Feb 24 2021 02:48:19

%S 0,1,2,2,4,4,8,10,8,4,8,12,12,16,28,30,16,4,8,12,12,16,28,32,20,16,28,

%T 36,40,60,88,78,32,4,8,12,12,16,28,32,20,16,28,36,40,60,88,80,36,16,

%U 28,36,40,60,88,84,56,60,92,112

%N Number of Q-toothpicks added at n-th stage to the structure of A187212.

%C Essentially the first differences of A187212.

%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 Nathaniel Johnston, <a href="http://www.nathanieljohnston.com/2011/03/the-q-toothpick-cellular-automaton/">The Q-Toothpick Cellular Automaton</a>

%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 It appears that if n = 2^k - 1, for k >= 2, then a(n) = A139251(n) - 2 otherwise a(n) = A139251(n). - Omar E. Pol, Mar 30 2011

%e Contribution from Omar E. Pol, Mar 29 2011 (Start):

%e If written as a triangle begins:

%e 0,

%e 1,

%e 2,

%e 2,4,

%e 4,8,10,8,

%e 4,8,12,12,16,28,30,16,

%e 4,8,12,12,16,28,32,20,16,28,36,40,60,88,78,32,

%e (End)

%Y Cf. A139250, A139251, A187211, A187212, A187221.

%K nonn

%O 0,3

%A _Omar E. Pol_, Mar 22 2011

%E Terms after a(24) from _Nathaniel Johnston_, Mar 28 2011