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

0,4

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

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

Example

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)

Mathematica

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

Crossrefs

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

Cf. A010060, A092255.

Sequence in context: A350287 A208888 A258783 * A050315 A128978 A325110

Adjacent sequences: A079315 A079316 A079317 * A079319 A079320 A079321

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 12 2003

Status

approved