

A079314


Number of firstquadrant cells (including the two boundaries) born at stage n of the HolladayUlam cellular automaton.


16



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, 28, 82, 28, 82, 82, 244, 2, 4, 4, 10, 4, 10, 10, 28, 4, 10, 10, 28, 10, 28, 28, 82, 4
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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 4fold 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. 27.


LINKS

Table of n, a(n) for n=0..80.
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)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. [From Omar E. Pol, Nov 20 2009]


EXAMPLE

Contribution 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)


CROSSREFS

Cf. A147582, A079315A079319, A151713, A139250.
Cf. A151922, A160407. [From Omar E. Pol, Nov 20 2009]
Sequence in context: A096865 A116466 A116467 * A323381 A060609 A330882
Adjacent sequences: A079311 A079312 A079313 * A079315 A079316 A079317


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Feb 12 2003


EXTENSIONS

Edited by N. J. A. Sloane, Aug 05 2009


STATUS

approved



