OFFSET
0,2
COMMENTS
See the main entry for this CA, A147562, for further information.
When I first read the Singmaster MS in 2003 I misunderstood the definition of the CA. In fact once cells are ON they stay ON. The other version, when cells can change state from ON to OFF, is described in A079317. - N. J. A. Sloane, Aug 05 2009
The pattern has 4-fold symmetry; sequence just counts cells in one quadrant.
REFERENCES
D. Singmaster, On the cellular automaton of Ulam and Warburton, M500 Magazine of the Open University, #195 (December 2003), pp. 2-7.
LINKS
Paolo Xausa, 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.]
Omar E. Pol, Illustration of initial terms (Overlapping squares) [From Omar E. Pol, Nov 20 2009]
D. 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
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015
FORMULA
For n > 0, a(n) = 3^(A000120(n)-1) + 1.
For n > 0, a(n) = A147582(n)/4 + 1.
Partial sums give A151922. [Omar E. Pol, Nov 20 2009]
EXAMPLE
From Omar E. Pol, Jul 18 2009: (Start)
If written as a triangle:
1;
2;
2,4;
2,4,4,10;
2,4,4,10,4,10,10,28;
2,4,4,10,4,10,10,28,4,10,10,28,10,28,28,82;
2,4,4,10,4,10,10,28,4,10,10,28,10,28,28,82,4,10,10,28,10,28,28,82,10,28;...
Rows converge to A151712.
(End)
MATHEMATICA
A079314list[nmax_]:=Join[{1}, 3^(DigitCount[Range[nmax], 2, 1]-1)+1]; A079314list[100] (* Paolo Xausa, Jun 29 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 12 2003
EXTENSIONS
Edited by N. J. A. Sloane, Aug 05 2009
STATUS
approved