This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A187564 #12 Feb 24 2021 02:48:19 %S A187564 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 A187564 50,86,58,142,210,262,2,6,10,22,10,30,50,78,10,30,50,86,58,142,210, %U A187564 262,10,30 %N A187564 Differences between the Gullwing sequence A187220 and A147562 (Ulam-Warburton cellular automaton). %C A187564 Apparently the Gullwing sequence A187220 is the connection between the Ulam-Warburton C. A. (A147562) and the toothpick sequence A139250. %C A187564 Note that the more complex structure is A187220, followed by A139250 and then A147562. %C A187564 For another version with minimal differences but asynchronous see A187223. %H A187564 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 A187564 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 A187564 a(n) = A187220(n) - A147562(n-1). %e A187564 If written as a triangle begins: %e A187564 1, %e A187564 2, %e A187564 2,6, %e A187564 2,6,10,22, %e A187564 2,6,10,22,10,30,50,78, %e A187564 2,6,10,22,10,30,50,78,10,30,50,86,58,142,210,262, %e A187564 2,6,10,22,10,30,50,78,10,30,50,86,58,142,210,262,10,30... %Y A187564 Cf. A139250, A147562, A187220, A187223. %K A187564 nonn %O A187564 1,2 %A A187564 _Omar E. Pol_, Mar 11 2011