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A231451
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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..3 introduced in row major order
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15
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2, 3, 6, 4, 15, 23, 7, 32, 97, 102, 12, 87, 340, 715, 492, 24, 229, 1598, 4179, 5643, 2485, 48, 647, 7429, 33659, 54868, 46075, 12858, 103, 1829, 38713, 265510, 738459, 741430, 382341, 67354, 222, 5293, 203544, 2308095, 9796477, 16471575, 10145989, 3196783
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OFFSET
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1,1
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COMMENTS
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Table starts
.......2.........3...........4.............7..............12.................24
.......6........15..........32............87.............229................647
......23........97.........340..........1598............7429..............38713
.....102.......715........4179.........33659..........265510............2308095
.....492......5643.......54868........738459.........9796477..........144109697
....2485.....46075......741430......16471575.......367351650.........9081622778
...12858....382341....10145989.....370059818.....13839802182.......572792301557
...67354...3196783...139597860....8337875579....522071407304.....36148438185936
..355003..26821757..1925134584..188061528227..19702443415959...2281891799253071
.1876862.225400759.26574209688.4243377409271.743668294490912.144055012148018656
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 11*a(n-1) -41*a(n-2) +65*a(n-3) -43*a(n-4) +9*a(n-5)
k=2: [order 7]
k=3: [order 17]
k=4: [order 25]
k=5: [order 65]
Empirical for row n:
n=1: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5)
n=2: [order 16]
n=3: [order 50] for n>51
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..1..1....0..0..1..1..0....0..0..0..1..1....0..0..1..1..1
..0..1..1..1..0....0..1..1..0..0....0..0..1..1..1....0..1..1..1..0
..1..1..1..0..0....1..2..2..0..0....0..1..2..2..0....0..0..0..0..2
..1..1..1..1..1....2..2..0..0..0....1..2..2..0..0....2..2..2..2..2
..0..0..0..0..0....3..3..3..3..3....0..0..0..0..0....1..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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