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A187223 Differences between A147562 (Ulam-Warburton cellular automaton) and A187220 (Gullwing sequence).

%I A187223 #16 Feb 24 2021 02:48:19
%S A187223 0,0,2,2,6,2,6,2,14,2,6,2,14,2,6,-14,30,2,6,2,14,2,6,-14,30,2,6,-14,
%T A187223 22,-22,-34,-102,62,2,6,2,14,2,6,-14,30,2,6,-14,22,-22,-34,-102,62,2,6
%N A187223 Differences between A147562 (Ulam-Warburton cellular automaton) and A187220 (Gullwing sequence).
%C A187223 Apparently the Gullwing sequence A187220 is the connection between the Ulam-Warburton C. A. (A147562) and the toothpick sequence A139250.
%C A187223 Note that the more complex structure is A187220, followed by A139250 and then A147562.
%C A187223 For another version which contains only positive terms and is more synchronous see the triangle A187564.
%H A187223 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 A187223 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 A187223 a(n) = A147562(n) - A187220(n).
%e A187223 Contribution from Omar E. Pol, Aug 25 2012 (Start):
%e A187223 Written as a triangle the sequence begins:
%e A187223 0,
%e A187223 0,
%e A187223 2,
%e A187223 2,6,
%e A187223 2,6,2,14,
%e A187223 2,6,2,14,2,6,-14,30,
%e A187223 2,6,2,14,2,6,-14,30,2,6,-14,22,-22,-34,-102,62,
%e A187223 2,6,2,14,2,6,-14,30,2,6,-14,22,-22,-34,-102,62,2,6,...
%e A187223 (End)
%Y A187223 Cf. A139250, A147562, A187220, A187564.
%K A187223 sign,tabf
%O A187223 0,3
%A A187223 _Omar E. Pol_, Mar 11 2011