Revision History for A305771
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| A305771
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Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
(history;
published version)
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#6 by Wesley Ivan Hurt at Sun May 26 01:05:58 EDT 2024
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#5 by Wesley Ivan Hurt at Sun May 26 01:05:48 EDT 2024
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| NAME
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Number of n X nX33 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
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| FORMULA
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Empirical: a(n) = 4*a(n-1) +a(n-2) -a(n-3) -20*a(n-4) -8*a(n-5) +26*a(n-6) +14*a(n-7) -12*a(n-8) +11*a(n-9) +23*a(n-10) -8*a(n-11) -24*a(n-12) -10*a(n-13) +7*a(n-14) -10*a(n-15) -8*a(n-16)).
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approved
editing
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#4 by R. H. Hardin at Sun Jun 10 09:40:02 EDT 2018
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#3 by R. H. Hardin at Sun Jun 10 09:39:59 EDT 2018
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| LINKS
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R. H. Hardin, <a href="/A305771/b305771.txt">Table of n, a(n) for n = 1..210</a>
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#2 by R. H. Hardin at Sun Jun 10 09:39:44 EDT 2018
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allocated for R. H. Hardin
Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
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| DATA
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4, 23, 81, 292, 1096, 4172, 15953, 61111, 234288, 898583, 3447045, 13224257, 50735544, 194653051, 746816146, 2865285427, 10993168588, 42177249636, 161820597240, 620853918472, 2382018289657, 9139044147504, 35063597098216
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| OFFSET
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1,1
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| COMMENTS
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Column 3 of A305776.
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| FORMULA
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Empirical: a(n) = 4*a(n-1) +a(n-2) -a(n-3) -20*a(n-4) -8*a(n-5) +26*a(n-6) +14*a(n-7) -12*a(n-8) +11*a(n-9) +23*a(n-10) -8*a(n-11) -24*a(n-12) -10*a(n-13) +7*a(n-14) -10*a(n-15) -8*a(n-16)
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| EXAMPLE
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Some solutions for n=5
..0..0..1. .0..1..1. .0..1..1. .0..1..1. .0..1..1. .0..1..0. .0..0..1
..0..1..0. .1..0..1. .0..1..0. .1..0..0. .1..0..1. .1..1..1. .0..0..0
..0..0..0. .1..1..1. .1..0..0. .1..0..1. .0..1..0. .0..1..1. .0..0..1
..1..0..0. .0..0..1. .0..1..0. .0..1..1. .0..1..0. .0..0..1. .1..0..0
..0..0..0. .1..0..0. .0..1..1. .0..0..0. .1..0..1. .1..0..1. .0..0..1
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| CROSSREFS
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Cf. A305776.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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R. H. Hardin, Jun 10 2018
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| STATUS
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approved
editing
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#1 by R. H. Hardin at Sun Jun 10 09:38:20 EDT 2018
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allocated for R. H. Hardin
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| KEYWORD
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allocated
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| STATUS
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approved
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