%I #18 Feb 24 2021 02:48:19

%S 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 32,56,72,80,120,176,160,64,8,16,24,24,32,56,64,40,32,56,72,80,120,

%U 176,160,72,32,56,72,80,120,176,168,112,120,184,224,280,416,512,384,128,8

%N First differences of A187220.

%C Number of gulls (or G-toothpicks) added at n-th stage to the gullwing structure of A187220.

%C Apparently this is the connection between A147582 and A139251. - Omar E. Pol, Mar 11 2011

%H David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>

%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(0)=0. a(1)=1. It appears that a(n) = 2*A139251(n-1), for n >= 2.

%e If written as an irregular triangle begins:

%e 0,

%e 1,

%e 2,

%e 4,

%e 8,8,

%e 8,16,24,16,

%e 8,16,24,24,32,56,64,32,

%e 8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,64,

%e ...

%e Also there is another version in which the layout of the irregular triangle was adjusted to reveal that the columns become constant:

%e .0,

%e .1,

%e .2,

%e .4,8,

%e .8,8,16,24,

%e 16,8,16,24,24,32,56,64,

%e 32,8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,

%e 64,8,16,24,24,32,56,64,40,32,56,72,80,120,176,160,72,32,56,72,80...

%Y Cf. A139250, A139251, A147582, A187211, A187220.

%K nonn

%O 0,3

%A _Omar E. Pol_, Mar 07 2011, Mar 09 2011