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A079318 a(0) = 1; for n > 0, a(n) = (3^(A000120(n)-1) + 1)/2. 4
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 (list; graph; refs; listen; history; text; internal format)
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
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]
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
Sequence in context: A350287 A208888 A258783 * A050315 A128978 A325110
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 12 2003
STATUS
approved

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Last modified May 21 19:35 EDT 2024. Contains 372738 sequences. (Running on oeis4.)