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Search: id:A079314
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| A079314 |
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Number of first-quadrant cells (including the two boundaries) born at stage n of the Holladay-Ulam cellular automaton. |
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+0
14
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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REFERENCES
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D. Singmaster, On the cellular automaton of Ulam and Warburton, unpublished manuscript, 2003.
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LINKS
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O. E. Pol, Illustration of initial terms (Overlapping squares) [From Omar E. Pol (info(AT)polprimos.com), Nov 20 2009]
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FORMULA
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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 (info(AT)polprimos.com), Nov 20 2009]
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EXAMPLE
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Contribution from Omar E. Pol (info(AT)polprimos.com), 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)
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CROSSREFS
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Cf. A147582, A079315-A079319, A151713, A139250.
Sequence in context: A096865 A116466 A116467 this_sequence A060609 A109526 A059214
Cf. A151922, A160407. [From Omar E. Pol (info(AT)polprimos.com), Nov 20 2009]
Adjacent sequences: A079311 A079312 A079313 this_sequence A079315 A079316 A079317
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KEYWORD
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nonn,easy,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 12 2003
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EXTENSIONS
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Edited by N. J. A. Sloane, Aug 05 2009
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