cp's OEIS Frontend

A173461 Number of cells turned "ON" at n-th stage of cellular automaton of A173460.

%I A173461 #27 Feb 24 2021 02:48:19
%S A173461 0,1,8,12,8,52,12,12,84,36,28,188,12,12,84,36,36,252,36,36,252,108,92,
%T A173461 628,12,12,84,36,36,252,36,36,252,108,108,756,36,36,252,108,108,756,
%U A173461 108,108,756,324,292,2012,12,12,84,36,36,252,36,36,252,108,108
%N A173461 Number of cells turned "ON" at n-th stage of cellular automaton of A173460.
%C A173461 Essentially the first differences of A173460.
%C A173461 It appears that row lengths give the absolute values of A110164. - _Omar E. Pol_, Apr 25 2013
%H A173461 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 A173461 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 A173461 a(0)=0, a(1)=1, a(2)=8, for n>=3 let i=n/3+1, j=A147610(i), if 2^r==i for some r then let c1=2^(r+1), c2=2^(r+4) else let c1=c2=0, finally when (n MOD 3)=0,1,2 let a(n)=12*j, 12*j-c1, 84*j-c2.  (Found empirically) [_Lars Blomberg_, Apr 23 2013]
%e A173461 From _Omar E. Pol_, Apr 25 2013: (Start)
%e A173461 When written as an irregular triangle begins:
%e A173461 0;
%e A173461 1,8;
%e A173461 12,8,52;
%e A173461 12,12,84,36,28,188;
%e A173461 12,12,84,36,36,252,36,36,252,108,92,628;
%e A173461 12,12,84,36,36,252,36,36,252,108,108,756,36,36,252,108,108,756,108,108,756,324,292,2012;
%e A173461 12,12,84,36,36,252,36,36,252,108,108,...
%e A173461 (End)
%Y A173461 Cf. A139250, A139251, A173457, A173460, A173462, A173463.
%K A173461 nonn,tabf
%O A173461 0,3
%A A173461 _Omar E. Pol_, Feb 18 2010
%E A173461 More terms a(14)-a(17) from _Omar E. Pol_, Sep 25 2011
%E A173461 a(18)-a(58) from _Lars Blomberg_, Apr 23 2013