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A279741
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T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
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14
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0, 0, 0, 2, 2, 0, 2, 6, 8, 0, 5, 14, 35, 26, 0, 8, 26, 106, 168, 80, 0, 15, 48, 286, 736, 766, 240, 0, 26, 84, 746, 2948, 4940, 3402, 708, 0, 46, 146, 1887, 11434, 29140, 32430, 14827, 2062, 0, 80, 250, 4700, 42494, 167904, 281350, 209558, 63680, 5944, 0, 139
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OFFSET
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1,4
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COMMENTS
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Table starts
.0.....0.......2........2..........5...........8............15..............26
.0.....2.......6.......14.........26..........48............84.............146
.0.....8......35......106........286.........746..........1887............4700
.0....26.....168......736.......2948.......11434.........42494..........154886
.0....80.....766.....4940......29140......167904........927615.........5029822
.0...240....3402....32430.....281350.....2407152......19743140.......158848594
.0...708...14827...209558....2672708....33954530.....413326300......4935790522
.0..2062...63680..1337624...25057618...472691878....8539248826....151323545378
.0..5944..270313..8453760..232453138..6511502806..174560480712...4589874672896
.0.16990.1136546.52990574.2137856646.88926626284.3537506044402.137999764109606
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 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) -35*a(n-2) +54*a(n-3) -45*a(n-4) +20*a(n-5) -4*a(n-6) for n>7
k=4: [order 16] for n>17
k=5: [order 25] for n>26
k=6: [order 64] for n>65
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
n=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
n=3: [order 16] for n>18
n=4: [order 45] for n>50
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..0
..1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..0. .0..1..1..0
..0..1..1..0. .0..0..0..1. .0..1..1..0. .0..1..1..0. .1..0..0..0
..0..1..0..1. .1..0..1..0. .0..0..1..1. .0..1..0..1. .0..1..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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