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A268995
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T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
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14
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2, 4, 4, 7, 13, 8, 13, 35, 41, 16, 23, 103, 174, 126, 32, 41, 278, 805, 849, 379, 64, 72, 763, 3331, 6009, 4083, 1121, 128, 126, 2037, 14080, 37987, 43512, 19416, 3272, 256, 219, 5421, 57287, 244397, 421450, 308112, 91491, 9449, 512, 379, 14264, 232449, 1506570
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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
....4....13......35.......103.........278...........763............2037
....8....41.....174.......805........3331.........14080...........57287
...16...126.....849......6009.......37987........244397.........1506570
...32...379....4083.....43512......421450.......4097199........38241770
...64..1121...19416....308112.....4583103......66954420.......946498448
..128..3272...91491...2144780....49084071....1073436321.....22995344760
..256..9449..427863..14730784...519385102...16957258387....550731432312
..512.27049.1988142.100087792..5442503771..264744926212..13040291111728
.1024.76866.9187653.674045392.56571775611.4093941136805.305911647779632
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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)
k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)
k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7
k=5: [order 8] for n>9
k=6: [order 10] for n>12
k=7: [order 14] for n>16
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6)
n=3: [order 9]
n=4: [order 16]
n=5: [order 26]
n=6: [order 42]
n=7: [order 68]
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EXAMPLE
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Some solutions for n=4 k=4
..1..1..0..1. .1..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..1
..0..0..0..1. .1..1..0..1. .0..1..0..0. .1..0..1..0. .0..0..0..1
..0..1..0..1. .0..0..0..0. .0..1..0..1. .1..0..0..0. .0..0..1..0
..0..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..1..0. .1..0..1..0
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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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