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A208085
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
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6
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8, 20, 12, 56, 20, 24, 164, 32, 56, 36, 488, 52, 134, 60, 72, 1460, 84, 344, 96, 168, 108, 4376, 136, 888, 156, 402, 180, 216, 13124, 220, 2318, 252, 1032, 288, 504, 324, 39368, 356, 6056, 408, 2664, 468, 1206, 540, 648, 118100, 576, 15848, 660, 6954, 756, 3096
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OFFSET
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1,1
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COMMENTS
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Table starts
...8..20...56..164..488..1460..4376..13124..39368.118100..354296.1062884
..12..20...32...52...84...136...220....356....576....932....1508....2440
..24..56..134..344..888..2318..6056..15848..41478.108584..284264..744206
..36..60...96..156..252...408...660...1068...1728...2796....4524....7320
..72.168..402.1032.2664..6954.18168..47544.124434.325752..852792.2232618
.108.180..288..468..756..1224..1980...3204...5184...8388...13572...21960
.216.504.1206.3096.7992.20862.54504.142632.373302.977256.2558376.6697854
.324.540..864.1404.2268..3672..5940...9612..15552..25164...40716...65880
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-2)
k=2..7: a(n) = 3*a(n-2) for n>3
Empirical for row n:
n=1: a(k)=4*a(k-1)-3*a(k-2)
n=2,4,6: a(k)=a(k-1)+a(k-2)
n=3,5,7: a(k)=3*a(k-1)-3*a(k-3)+a(k-4)
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EXAMPLE
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Some solutions for n=4 k=3
..0..1..0..0....0..1..0..1....0..0..0..0....0..1..1..1....0..0..0..0
..0..1..0..1....0..0..0..0....1..1..1..1....0..1..0..1....1..0..1..0
..1..0..1..0....0..0..0..0....1..1..1..1....1..0..1..0....0..1..0..1
..1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0....0..0..0..0
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..0..0..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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