A187223 - OEIS

%I #16 Feb 24 2021 02:48:19

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

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

%C Apparently the Gullwing sequence A187220 is the connection between the Ulam-Warburton C. A. (A147562) and the toothpick sequence A139250.

%C Note that the more complex structure is A187220, followed by A139250 and then A147562.

%C For another version which contains only positive terms and is more synchronous see the triangle A187564.

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

%e Contribution from Omar E. Pol, Aug 25 2012 (Start):

%e Written as a triangle the sequence begins:

%e 0,

%e 0,

%e 2,

%e 2,6,

%e 2,6,2,14,

%e 2,6,2,14,2,6,-14,30,

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

%e 2,6,2,14,2,6,-14,30,2,6,-14,22,-22,-34,-102,62,2,6,...

%e (End)

%Y Cf. A139250, A147562, A187220, A187564.

%K sign,tabf

%O 0,3

%A _Omar E. Pol_, Mar 11 2011