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| A273570
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Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 798", based on the 5-celled von Neumann neighborhood.
(history;
published version)
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#15 by Charles R Greathouse IV at Fri Jul 26 21:16:43 EDT 2024
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| NAME
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Number of active (ON,, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 798", based on the 5-celled von Neumann neighborhood.
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Discussion
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| Fri Jul 26
| 21:16
| OEIS Server: https://oeis.org/edit/global/2997
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#14 by Michel Marcus at Thu Dec 01 14:40:37 EST 2016
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#13 by Michel Marcus at Thu Dec 01 14:40:33 EST 2016
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| LINKS
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N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.
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| STATUS
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reviewed
editing
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#12 by Joerg Arndt at Thu Dec 01 12:53:19 EST 2016
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#11 by Colin Barker at Thu Dec 01 12:00:50 EST 2016
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#10 by Colin Barker at Thu Dec 01 11:55:00 EST 2016
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| FORMULA
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Conjectures from Colin Barker, Dec 01 2016: (Start)
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>4.
G.f.: (1 - 2*x + 8*x^3 + 32*x^4) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).
(End)
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| STATUS
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approved
editing
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#9 by Peter Luschny at Thu Jul 21 02:00:43 EDT 2016
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#8 by Michel Marcus at Thu Jul 21 01:46:45 EDT 2016
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#7 by Lars Blomberg at Thu Jul 21 01:40:08 EDT 2016
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#6 by Lars Blomberg at Thu Jul 21 01:36:24 EDT 2016
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| DATA
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1, 5, 21, 93, 429, 1869, 7821, 32013, 129549, 521229, 2091021, 8376333, 33529869, 134168589, 536772621, 2147287053
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| COMMENTS
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Conjecture: Rule 862 also generates this sequence. - Lars Blomberg, Jul 21 2016
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| FORMULA
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Conjecture: a(n) = 2*4^n - 6*2^n + 13, n>1. - Lars Blomberg, Jul 21 2016
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| EXTENSIONS
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a(8)-a(15) from Lars Blomberg, Jul 21 2016
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| STATUS
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approved
editing
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