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A268781
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T(n,k) = Number of n X k binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.
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8
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2, 4, 4, 7, 11, 7, 13, 26, 26, 13, 23, 65, 91, 65, 23, 41, 148, 316, 316, 148, 41, 72, 343, 1031, 1462, 1031, 343, 72, 126, 766, 3354, 6383, 6383, 3354, 766, 126, 219, 1709, 10615, 27531, 38483, 27531, 10615, 1709, 219, 379, 3752, 33344, 115391, 224960
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OFFSET
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1,1
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COMMENTS
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Table starts
...2....4......7......13........23.........41...........72...........126
...4...11.....26......65.......148........343..........766..........1709
...7...26.....91.....316......1031.......3354........10615.........33344
..13...65....316....1462......6383......27531.......115391........478849
..23..148...1031....6383.....38483.....224960......1288693.......7271509
..41..343...3354...27531....224960....1755113.....13493468.....101738555
..72..766..10615..115391...1288693...13493468....140404442....1425678976
.126.1709..33344..478849...7271509..101738555...1425678976...19400886875
.219.3752.103339.1957904..40511381..758303322..14341399141..262072220011
.379.8195.317958.7940136.223527424.5590121407.142487073304.3491534799847
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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).
k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4).
k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6).
k=4: [order 8].
k=5: [order 12].
k=6: [order 16].
k=7: [order 28].
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EXAMPLE
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Some solutions for n=4, k=4
..0..0..0..0. .1..0..0..1. .1..0..1..1. .0..1..0..1. .0..1..0..0
..1..0..1..1. .0..0..1..0. .0..0..0..0. .1..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..1..0..0. .1..0..1..0. .1..0..1..0. .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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