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A187221 First differences of A187220.

%I A187221 #18 Feb 24 2021 02:48:19
%S A187221 0,1,2,4,8,8,8,16,24,16,8,16,24,24,32,56,64,32,8,16,24,24,32,56,64,40,
%T A187221 32,56,72,80,120,176,160,64,8,16,24,24,32,56,64,40,32,56,72,80,120,
%U A187221 176,160,72,32,56,72,80,120,176,168,112,120,184,224,280,416,512,384,128,8
%N A187221 First differences of A187220.
%C A187221 Number of gulls (or G-toothpicks) added at n-th stage to the gullwing structure of A187220.
%C A187221 Apparently this is the connection between A147582 and A139251. - Omar E. Pol, Mar 11 2011
%H A187221 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A187221 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 A187221 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 A187221 a(0)=0. a(1)=1. It appears that a(n) = 2*A139251(n-1), for n >= 2.
%e A187221 If written as an irregular triangle begins:
%e A187221 0,
%e A187221 1,
%e A187221 2,
%e A187221 4,
%e A187221 8,8,
%e A187221 8,16,24,16,
%e A187221 8,16,24,24,32,56,64,32,
%e A187221 8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,64,
%e A187221 ...
%e A187221 Also there is another version in which the layout of the irregular triangle was adjusted to reveal that the columns become constant:
%e A187221 .0,
%e A187221 .1,
%e A187221 .2,
%e A187221 .4,8,
%e A187221 .8,8,16,24,
%e A187221 16,8,16,24,24,32,56,64,
%e A187221 32,8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,
%e A187221 64,8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,72,32,56,72,80...
%Y A187221 Cf. A139250, A139251, A147582, A187211, A187220.
%K A187221 nonn
%O A187221 0,3
%A A187221 _Omar E. Pol_, Mar 07 2011, Mar 09 2011