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A297607
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T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.
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13
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2, 4, 4, 7, 11, 8, 13, 35, 35, 16, 24, 96, 181, 106, 32, 44, 281, 787, 953, 327, 64, 81, 829, 3691, 6413, 4997, 1003, 128, 149, 2428, 17186, 49198, 52512, 26155, 3082, 256, 274, 7059, 80140, 368007, 654033, 429491, 137033, 9465, 512, 504, 20611, 371557
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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..........24............44..............81
...4....11......35........96.........281...........829............2428
...8....35.....181.......787........3691.........17186...........80140
..16...106.....953......6413.......49198........368007.........2781983
..32...327....4997.....52512......654033.......7847849........95770934
..64..1003...26155....429491.....8689859.....167209522......3295502717
.128..3082..137033...3514058...115571432....3567494618....113592447685
.256..9465..717905..28752016..1536728161...76095857063...3914150992637
.512.29073.3760657.235246416.20433704585.1623142226575.134873268392766
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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) = 2*a(n-1) +3*a(n-2) +a(n-3) -a(n-5)
k=3: [order 11]
k=4: [order 32]
k=5: [order 55]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) +a(n-3)
n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +12*a(n-4) -12*a(n-6)
n=3: [order 13]
n=4: [order 34]
n=5: [order 96]
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EXAMPLE
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Some solutions for n=4 k=4
..1..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0. .1..0..1..1
..0..0..1..0. .1..0..0..1. .1..0..1..0. .0..0..0..1. .1..0..0..0
..0..0..0..0. .0..1..0..1. .1..0..0..0. .0..0..0..0. .0..0..0..1
..1..0..1..1. .0..1..0..1. .0..0..1..1. .0..1..0..0. .0..1..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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