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%I #26 Aug 01 2023 07:54:34
%S 0,1,6,16,16,40,16,40,40,112,16,40,40,112,40,112,112,328,16,40,40,112,
%T 40,112,112,328,40,112,112,328,112,328,328,976,16,40,40,112,40,112,
%U 112,328,40,112,112,328,112,328,328,976,40,112,112,328,112,328,328,976
%N Number of toothpicks added at n-th stage to the toothpick structure of A183126.
%C Essentially the first differences of A183126.
%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) = 4*(1 + 3^A000120(n-2)), n >= 3. - _Nathaniel Johnston_, Apr 06 2011
%t a[n_] := 4*(1 + 3^DigitCount[n-2, 2, 1]); a[0] = 0; a[1] = 1; a[2] = 6; Array[a, 100, 0] (* _Amiram Eldar_, Aug 01 2023 *)
%Y Cf. A000120, A139250, A139251, A160173, A161411, A183126, A183149.
%K nonn
%O 0,3
%A _Omar E. Pol_, Mar 28 2011
%E a(0)-a(10) confirmed and a(11)-a(35) added by _John W. Layman_, Mar 30 2011
%E a(36)-a(47) from _Nathaniel Johnston_, Apr 06 2011
%E More terms from _Amiram Eldar_, Aug 01 2023
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