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| A273565
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Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 793", based on the 5-celled von Neumann neighborhood.
(history;
published version)
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#13 by Charles R Greathouse IV at Fri Jul 26 21:16:43 EDT 2024
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Number of active (ON,, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 793", 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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#12 by Bruno Berselli at Thu Dec 01 11:57:51 EST 2016
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#11 by Colin Barker at Thu Dec 01 11:51:25 EST 2016
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#10 by Colin Barker at Thu Dec 01 11:51:07 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 - 3*x + 14*x^2 - 7*x^3 - 2*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 02:00:37 EDT 2016
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#8 by Michel Marcus at Thu Jul 21 01:46:23 EDT 2016
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#7 by Lars Blomberg at Thu Jul 21 01:40:04 EDT 2016
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#6 by Lars Blomberg at Thu Jul 21 01:33:47 EDT 2016
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| DATA
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1, 4, 28, 141, 625, 2625, 10753, 43521, 175105, 702465, 2813953, 11264001, 45072385, 180322305, 721354753, 2885550081
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| FORMULA
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Conjecture: a(n) = 43*4^(n-2) - 4*2^n + 1, 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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#5 by Bruno Berselli at Wed May 25 10:12:35 EDT 2016
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#4 by Michel Marcus at Wed May 25 10:10:41 EDT 2016
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