A187564 -id:A187564 - cp's OEIS frontend

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

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, 22, -22, -34, -102, 62, 2, 6, 2, 14, 2, 6, -14, 30, 2, 6, -14, 22, -22, -34, -102, 62, 2, 6

Offset: 0

Omar E. Pol, Mar 11 2011

Apparently the Gullwing sequence A187220 is the connection between the Ulam-Warburton C. A. (A147562) and the toothpick sequence A139250.
Note that the more complex structure is A187220, followed by A139250 and then A147562.
For another version which contains only positive terms and is more synchronous see the triangle A187564.

			Contribution from Omar E. Pol, Aug 25 2012 (Start):
Written as a triangle the sequence begins:
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,-14,22,-22,-34,-102,62,
2,6,2,14,2,6,-14,30,2,6,-14,22,-22,-34,-102,62,2,6,...
(End)

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, 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.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Cf. A139250, A147562, A187220, A187564.

a(n) = A147562(n) - A187220(n).

cp's OEIS Frontend

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

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