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

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Feb 12 2003

Keywords

• nonn
• easy

Examples

			From _Omar E. Pol_, Jul 18 2009: (Start)
If written as a triangle:
1;
1;
1,2;
1,2,2,5;
1,2,2,5,2,5,5,14;
1,2,2,5,2,5,5,14,2,5,5,14,5,14,14,41;
1,2,2,5,2,5,5,14,2,5,5,14,5,14,14,41,2,5,5,14,5,14,14,41,5,14,14,41,14,41,41,122;
(End)
		

References

• Alex Fink, Aviezri S. Fraenkel and Carlos Santos, LIM is not slim, International Journal of Game Theory, May 2013
• David Singmaster, On the cellular automaton of Ulam and Warburton, M500 Magazine of the Open University, #195 (December 2003), pp. 2-7.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, 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.]
• David Singmaster, On the cellular automaton of Ulam and Warburton, 2003 [Cached copy, included with permission]
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Cf. A079314, A079315, A079316, A079317, A079318, A079319.

Cf. A010060, A092255.

Programs

Mathematica

a[n_] := (3^(DigitCount[n, 2, 1] - 1) + 1)/2; a[0] = 1; Array[a, 100, 0] (* Amiram Eldar, Jul 29 2023 *)

Formula

For n>=1, a(n) mod 2 = A010060(n), the Thue-Morse sequence - Benoit Cloitre, Mar 23 2004

a(n) = Sum_{i+j+k=n, 0<=k<=j<=i<=n} (n!/(i!*j!*k!) mod 2). - Benoit Cloitre, Jul 02 2004