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A279158
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T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
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7
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0, 0, 0, 2, 0, 2, 2, 4, 4, 2, 5, 12, 20, 12, 5, 8, 30, 72, 72, 30, 8, 15, 72, 255, 428, 255, 72, 15, 26, 162, 874, 2294, 2294, 874, 162, 26, 46, 356, 2903, 11932, 20104, 11932, 2903, 356, 46, 80, 766, 9336, 60304, 166552, 166552, 60304, 9336, 766, 80, 139, 1616, 29578
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OFFSET
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1,4
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COMMENTS
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Table starts
..0....0.....2.......2.........5...........8............15..............26
..0....0.....4......12........30..........72...........162.............356
..2....4....20......72.......255.........874..........2903............9336
..2...12....72.....428......2294.......11932.........60304..........297092
..5...30...255....2294.....20104......166552.......1331471........10508084
..8...72...874...11932....166552.....2145788......26724386.......330704288
.15..162..2903...60304...1331471....26724386.....517476726.....10025433990
.26..356..9336..297092..10508084...330704288...10025433990....305617345164
.46..766.29578.1443498..81594334..4027185426..191191601644...9168921176076
.80.1616.92528.6930508.624717186.48341053840.3592564336954.270873567300596
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
k=2: a(n) = 4*a(n-1) -5*a(n-2) +6*a(n-3) -12*a(n-4) +8*a(n-5) -4*a(n-6) +8*a(n-7)
k=3: [order 22] for n>23
k=4: [order 56] for n>57
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1. .0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..0
..0..0..1..0. .0..0..1..0. .1..0..1..1. .0..1..0..1. .0..0..1..1
..1..1..0..1. .1..1..0..1. .1..0..0..0. .1..1..0..1. .1..1..0..0
..0..0..1..0. .0..1..0..1. .1..0..1..1. .0..0..0..1. .0..1..0..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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