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A173457 Number of cell turned "ON" at n-th stage of cellular automaton of A173456.

%I A173457 #22 Feb 24 2021 02:48:19
%S A173457 0,1,8,12,4,28,36,4,28,36,12,84,108,4,28,36,12,84,108,12,84,108,36,
%T A173457 252,324,4,28,36,12,84,108,12,84,108,36,252,324,12,84,108,36,252,324,
%U A173457 36,252,324,108,756,972,4,28,36,12,84,108,12,84,108,36,252,324
%N A173457 Number of cell turned "ON" at n-th stage of cellular automaton of A173456.
%C A173457 Essentially the first differences of A173456.
%C A173457 It appears that row lengths give A098011. After the initial zero, it appears that row lengths give the absolute values of A110164. - _Omar E. Pol_, Apr 22 2013
%H A173457 Lars Blomberg, <a href="/A173457/b173457.txt">Table of n, a(n) for n = 0..6000</a>
%H A173457 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 A173457 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 A173457 a(0)=0, a(1)=1, a(2)=8, a(3)=12, for n>=4 when (n MOD 3)=0,1,2 let m=36,4,28 then a(n)=m*A147610((n + 2) / 3). (Found empirically) [_Lars Blomberg_, Apr 22 2013]
%e A173457 From Omar E. Pol, Apr 22 2013 (Start):
%e A173457 When written as an irregular triangle begins:
%e A173457 0;
%e A173457 1;
%e A173457 8,12;
%e A173457 4,28,36;
%e A173457 4,28,36,12,84,108;
%e A173457 4,28,36,12,84,108,12,84,108,36,252,324;
%e A173457 4,28,36,12,84,108,12,84,108,36,252,324,12,84,108,36,252,324,36,252,324,108,756,972;
%e A173457 4,28,36,12,84,108,12,84,108,36,252,324,...
%e A173457 (End)
%Y A173457 Cf. A139250, A139251, A173456, A173458, A173459, A173461.
%K A173457 nonn,tabf
%O A173457 0,3
%A A173457 _Omar E. Pol_, Feb 18 2010
%E A173457 a(41)-a(60) from _Lars Blomberg_, Apr 22 2013