Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #27 Feb 24 2021 02:48:19
%S 0,1,8,12,8,52,12,12,84,36,28,188,12,12,84,36,36,252,36,36,252,108,92,
%T 628,12,12,84,36,36,252,36,36,252,108,108,756,36,36,252,108,108,756,
%U 108,108,756,324,292,2012,12,12,84,36,36,252,36,36,252,108,108
%N Number of cells turned "ON" at n-th stage of cellular automaton of A173460.
%C Essentially the first differences of A173460.
%C It appears that row lengths give the absolute values of A110164. - _Omar E. Pol_, Apr 25 2013
%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, 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 From _Omar E. Pol_, Apr 25 2013: (Start)
%e When written as an irregular triangle begins:
%e 0;
%e 1,8;
%e 12,8,52;
%e 12,12,84,36,28,188;
%e 12,12,84,36,36,252,36,36,252,108,92,628;
%e 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 12,12,84,36,36,252,36,36,252,108,108,...
%e (End)
%Y Cf. A139250, A139251, A173457, A173460, A173462, A173463.
%K nonn,tabf
%O 0,3
%A _Omar E. Pol_, Feb 18 2010
%E More terms a(14)-a(17) from _Omar E. Pol_, Sep 25 2011
%E a(18)-a(58) from _Lars Blomberg_, Apr 23 2013