A187564 - OEIS

%I #12 Feb 24 2021 02:48:19

%S 1,2,2,6,2,6,10,22,2,6,10,22,10,30,50,78,2,6,10,22,10,30,50,78,10,30,

%T 50,86,58,142,210,262,2,6,10,22,10,30,50,78,10,30,50,86,58,142,210,

%U 262,10,30

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

%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 with minimal differences but asynchronous see A187223.

%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) = A187220(n) - A147562(n-1).

%e If written as a triangle begins:

%e 1,

%e 2,

%e 2,6,

%e 2,6,10,22,

%e 2,6,10,22,10,30,50,78,

%e 2,6,10,22,10,30,50,78,10,30,50,86,58,142,210,262,

%e 2,6,10,22,10,30,50,78,10,30,50,86,58,142,210,262,10,30...

%Y Cf. A139250, A147562, A187220, A187223.

%K nonn

%O 1,2

%A _Omar E. Pol_, Mar 11 2011