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A079318 a(0) = 1; for n > 0, a(n) = (3^(A000120(n)-1) + 1)/2.

%I A079318 #31 Jul 29 2023 03:14:03
%S A079318 1,1,1,2,1,2,2,5,1,2,2,5,2,5,5,14,1,2,2,5,2,5,5,14,2,5,5,14,5,14,14,
%T A079318 41,1,2,2,5,2,5,5,14,2,5,5,14,5,14,14,41,2,5,5,14,5,14,14,41,5,14,14,
%U A079318 41,14,41,41,122,1,2,2,5,2,5,5,14,2,5,5,14,5,14,14,41,2,5,5,14,5,14,14,41,5,14,14
%N A079318 a(0) = 1; for n > 0, a(n) = (3^(A000120(n)-1) + 1)/2.
%D A079318 Alex Fink, Aviezri S. Fraenkel and Carlos Santos, LIM is not slim, International Journal of Game Theory, May 2013
%D A079318 David Singmaster, On the cellular automaton of Ulam and Warburton, M500 Magazine of the Open University, #195 (December 2003), pp. 2-7.
%H A079318 Amiram Eldar, <a href="/A079318/b079318.txt">Table of n, a(n) for n = 0..10000</a>
%H A079318 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 A079318 David Singmaster, <a href="/A079314/a079314.pdf">On the cellular automaton of Ulam and Warburton</a>, 2003 [Cached copy, included with permission]
%H A079318 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 A079318 For n>=1, a(n) mod 2 = A010060(n), the Thue-Morse sequence - _Benoit Cloitre_, Mar 23 2004
%F A079318 a(n) = Sum_{i+j+k=n, 0<=k<=j<=i<=n} (n!/(i!*j!*k!) mod 2). - _Benoit Cloitre_, Jul 02 2004
%e A079318 From _Omar E. Pol_, Jul 18 2009: (Start)
%e A079318 If written as a triangle:
%e A079318 1;
%e A079318 1;
%e A079318 1,2;
%e A079318 1,2,2,5;
%e A079318 1,2,2,5,2,5,5,14;
%e A079318 1,2,2,5,2,5,5,14,2,5,5,14,5,14,14,41;
%e A079318 1,2,2,5,2,5,5,14,2,5,5,14,5,14,14,41,2,5,5,14,5,14,14,41,5,14,14,41,14,41,41,122;
%e A079318 (End)
%t A079318 a[n_] := (3^(DigitCount[n, 2, 1] - 1) + 1)/2; a[0] = 1; Array[a, 100, 0] (* _Amiram Eldar_, Jul 29 2023 *)
%Y A079318 Cf. A079314, A079315, A079316, A079317, A079318, A079319.
%Y A079318 Cf. A010060, A092255.
%K A079318 nonn,easy
%O A079318 0,4
%A A079318 _N. J. A. Sloane_, Feb 12 2003