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A190033
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T(n,k)=Number of (n+2)X(k+2) binary arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock
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10
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512, 112, 112, 228, 45, 228, 415, 79, 79, 415, 616, 155, 158, 155, 616, 880, 235, 274, 274, 235, 880, 1205, 295, 362, 458, 362, 295, 1205, 1508, 355, 430, 578, 578, 430, 355, 1508, 2008, 423, 506, 670, 834, 670, 506, 423, 2008, 2793, 531, 610, 790, 970, 970, 790
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OFFSET
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1,1
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COMMENTS
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Table starts
..512.112..228..415..616..880.1205.1508.2008.2793..3776..5220..7274..9829.13345
..112..45...79..155..235..295..355..423..531..740..1037..1434..1992..2706..3628
..228..79..158..274..362..430..506..610..790.1094..1539..2128..2917..3951..5309
..415.155..274..458..578..670..790..966.1242.1702..2338..3247..4460..6025..8139
..616.235..362..578..834..970.1162.1418.1802.2446..3314..4446..6199..8432.11313
..880.295..430..670..970.1230.1494.1834.2338.3142..4226..5674..7686.10543.14268
.1205.355..506..790.1162.1494.1910.2362.3002.4006..5390..7234..9790.13178.17955
.1508.423..610..966.1418.1834.2362.3018.3834.5122..6886..9242.12530.16874.22626
.2008.531..790.1242.1802.2338.3002.3834.5102.6794..9110.12238.16562.22266.29874
.2793.740.1094.1702.2446.3142.4006.5122.6794.9706.12930.17246.23194.31074.41542
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LINKS
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FORMULA
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Empirical for all columns: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>11,10,11,12,13,14,15,16 respectively for k=1..8
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EXAMPLE
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Some solutions for 5X4
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1....1..1..1..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..0..0....0..0..0..0....0..0..0..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
..1..1..0..0....0..0..0..0....0..0..0..1....0..0..0..0....1..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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