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Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose virtual skeleton is a polyedge as the toothpick structure of A139250 but with toothpicks of length 6.
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%I #9 Feb 24 2021 02:48:18

%S 0,7,19,41,63,87,131,193,235,259,303,367,435,527,675,837,919,943,987,

%T 1051,1119,1211,1359,1523,1631,1723,1875,2071,2299,2631,3087,3489,

%U 3651,3675,3719,3783,3851,3943,4091,4255,4363,4455,4607,4803,5031,5363,5819,6223,6411

%N Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose virtual skeleton is a polyedge as the toothpick structure of A139250 but with toothpicks of length 6.

%C a(n) is also the number of grid points that are covered after n-th stage by an polyedge as the toothpick structure of A139250, but with toothpicks of length 6.

%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) = A147614(n)+4*A139250(n) = A160420(n)+2*A139250(n) since each toothpick covers exactly four more grid points than the corresponding toothpick in A147614.

%Y Cf. A139250, A139251, A147614, A160118, A160120, A160170, A160420, A160430.

%K nonn

%O 0,2

%A _Omar E. Pol_, May 20 2009

%E More terms and formula from _Nathaniel Johnston_, Nov 13 2010