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A231997
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to one
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14
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4, 6, 9, 16, 32, 25, 39, 121, 156, 64, 81, 406, 1024, 800, 169, 168, 1225, 5778, 8464, 4000, 441, 361, 3916, 28900, 80511, 70225, 20228, 1156, 780, 12769, 155496, 674041, 1129755, 582169, 101808, 3025, 1681, 41180, 863041, 6257919, 15594601, 15851094
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OFFSET
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1,1
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COMMENTS
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Table starts
.....4........6.........16...........39..............81...............168
.....9.......32........121..........406............1225..............3916
....25......156.......1024.........5778...........28900............155496
....64......800.......8464........80511..........674041...........6257919
...169.....4000......70225......1129755........15594601.........245403000
...441....20228.....582169.....15851094.......362293156........9716967198
..1156...101808....4826809....222394359......8404672329......383555570610
..3025...513400...40018276...3120433160....195072388900....15154710590391
..7921..2586980..331786225..43782113196...4526898777801...598600429698510
.20736.13039568.2750792704.614302069661.105058031047524.23646568415709520
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..418
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
k=2: a(n) = 3*a(n-1) +12*a(n-2) -5*a(n-3) -19*a(n-4) +2*a(n-5) +4*a(n-6)
k=3: a(n) = 9*a(n-1) -3*a(n-2) -25*a(n-3) +9*a(n-4) +3*a(n-5) -a(n-6)
k=4: [order 14]
k=5: [order 36]
k=6: [order 90] for n>91
Empirical for row n:
n=1: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) -2*a(n-8) -a(n-9)
n=2: [order 15]
n=3: [order 36] for n>38
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1..1....1..0..0..1..1....0..0..1..0..0....1..0..0..0..0
..0..0..0..0..1....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0
..0..1..0..1..0....0..1..1..0..1....1..0..0..0..0....0..1..0..0..0
..1..0..1..0..0....0..0..0..1..1....1..0..1..1..0....0..0..0..1..0
..0..1..0..0..1....1..0..0..0..0....0..0..0..0..1....1..0..0..0..1
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CROSSREFS
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Column 1 is A007598(n+2)
Column 3 is A217022(n+1)
Sequence in context: A225377 A036667 A056016 * A220144 A346591 A152002
Adjacent sequences: A231994 A231995 A231996 * A231998 A231999 A232000
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Nov 16 2013
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STATUS
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approved
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