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A280161
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T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal 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, 4, 2, 2, 8, 8, 2, 5, 18, 31, 18, 5, 8, 40, 94, 94, 40, 8, 15, 92, 305, 424, 305, 92, 15, 26, 208, 950, 1854, 1854, 950, 208, 26, 46, 470, 2901, 7628, 10677, 7628, 2901, 470, 46, 80, 1060, 8728, 30874, 58852, 58852, 30874, 8728, 1060, 80, 139, 2384, 26068
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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...........46
..0....4.....8.....18......40........92........208.........470.........1060
..2....8....31.....94.....305.......950.......2901........8728........26068
..2...18....94....424....1854......7628......30874......123312.......488256
..5...40...305...1854...10677.....58852.....318220.....1695030......8941285
..8...92...950...7628...58852....434790....3138340....22348406....157294986
.15..208..2901..30874..318220...3138340...30089398...285461736...2671391625
.26..470..8728.123312.1695030..22348406..285461736..3612425586..45045404794
.46.1060.26068.488256.8941285.157294986.2671391625.45045404794.748382706193
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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) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) for n>8
k=3: [order 14] for n>19
k=4: [order 30] for n>36
k=5: [order 70] for n>80
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..0..0
..0..1..0..1. .0..0..0..1. .0..1..1..0. .0..0..1..1. .1..1..0..1
..1..1..1..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .1..0..1..1
..1..1..0..0. .1..1..1..1. .0..1..0..0. .0..1..0..0. .0..0..1..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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