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A250277
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T(n,k)=Number of length n+1 0..k arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero
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12
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2, 3, 4, 4, 11, 8, 5, 20, 27, 16, 6, 33, 52, 79, 32, 7, 48, 89, 240, 255, 64, 8, 67, 140, 581, 984, 843, 128, 9, 88, 207, 1132, 2909, 4412, 2763, 256, 10, 113, 288, 1991, 6732, 17885, 20252, 8903, 512, 11, 140, 389, 3156, 14003, 51884, 107387, 91808, 28215, 1024, 12
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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........5.........6.........7..........8...........9
....4....11......20.......33........48........67.........88.........113
....8....27......52.......89.......140.......207........288.........389
...16....79.....240......581......1132......1991.......3156........4841
...32...255.....984.....2909......6732.....14003......25964.......45303
...64...843....4412....17885.....51884....130335.....281552......564985
..128..2763...20252...107387....381812...1154141....2908232.....6704631
..256..8903...91808...636197...2783500..10172515...30143732....80256473
..512.28215..406748..3664311..19762916..86975297..301550620...925066871
.1024.88195.1759740.20397261.135821156.715749943.2901853512.10244309701
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5) for n>6
k=3: [order 15] for n>18
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2
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EXAMPLE
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Some solutions for n=6 k=4
..4....0....0....1....3....3....4....3....3....1....2....0....4....1....3....3
..2....2....0....1....1....3....2....3....2....4....3....3....4....3....2....4
..4....2....2....4....2....3....0....3....4....4....0....2....4....2....2....4
..2....1....4....4....1....3....4....1....2....1....2....4....2....3....1....2
..2....2....4....2....1....1....4....0....1....2....4....3....1....1....1....4
..2....3....2....1....1....3....2....1....2....1....3....4....2....1....0....0
..4....2....0....3....3....3....0....3....3....1....0....2....4....1....1....3
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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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