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A231764
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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, diagonal and antidiagonal neighbors equal to one
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15
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9, 33, 16, 100, 136, 36, 315, 625, 660, 81, 961, 2976, 5041, 3213, 169, 3024, 15625, 38160, 40000, 14989, 361, 9409, 84817, 356409, 493695, 303601, 70927, 784, 29319, 440896, 3453471, 8231161, 5879679, 2353156, 338352, 1681, 91204, 2280000
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OFFSET
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1,1
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COMMENTS
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Table starts
....9.......33........100...........315.............961...............3024
...16......136........625..........2976...........15625..............84817
...36......660.......5041.........38160..........356409............3453471
...81.....3213......40000........493695.........8231161..........143424652
..169....14989.....303601.......5879679.......175642009.........5493044921
..361....70927....2353156......71884125......3855664836.......216545491864
..784...338352...18318400.....893571840.....85629975876......8624298007460
.1681..1603633..141681409...10965349591...1881009507001....340129511751843
.3600..7596720.1096603225..134407778400..41320353904281..13416072442152345
.7744.36066272.8501393209.1654812479232.910635938795025.530629269304561623
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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) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)
k=2: [order 21]
k=3: [order 45]
Empirical for row n:
n=1: a(n) = 3*a(n-1) +a(n-3) +7*a(n-4) -20*a(n-5) -2*a(n-6) -4*a(n-8) +8*a(n-9)
n=2: [order 36]
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..0..1..1....1..1..1..0..1....0..0..0..0..1....0..1..1..1..0
..1..0..0..0..0....0..0..0..1..0....0..0..1..0..0....0..0..1..0..0
..1..0..0..0..1....0..0..0..0..0....0..0..0..1..1....1..0..0..0..0
..1..0..0..0..0....0..0..0..0..0....1..1..0..0..1....1..0..0..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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