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A195232
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T(n,k)is the number of lower triangles of an n X n 0..k array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less
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12
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2, 3, 8, 4, 15, 64, 5, 22, 155, 1024, 6, 29, 246, 3151, 32768, 7, 36, 337, 5428, 127785, 2097152, 8, 43, 428, 7705, 237818, 10322065, 268435456, 9, 50, 519, 9982, 348849, 20729610, 1663418313, 68719476736, 10, 57, 610, 12259, 459880, 31374671
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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
...........8...........15............22............29............36
..........64..........155...........246...........337...........428
........1024.........3151..........5428..........7705..........9982
.......32768.......127785........237818........348849........459880
.....2097152.....10322065......20729610......31374671......42029278
...268435456...1663418313....3601738548....5618308863....7640055854
.68719476736.535153390177.1249159521262.2006626824777.2767861764930
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..205
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FORMULA
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Empirical for rows:
T(1,k) = 1*k + 1
T(2,k) = 7*k + 1
T(3,k) = 91*k - 27
T(4,k) = 2277*k - 1403 for k>1
T(5,k) = 111031*k - 95275 for k>2
T(6,k) = 10654607*k - 11243757 for k>3
T(7,k) = 2021888119*k - 2469384741 for k>4
Generalizing, T(n,k) = A195213(n) + const(n) for k>n-3
Since elements of a solution differ by no more than n, T(n,k)-T(n,k-1) is constant for k >= n. This confirms the empirical formula: T(n,k) is a polynomial of degree 1 in k for k > n-3. - Robert Israel, Nov 21 2017
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EXAMPLE
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Some solutions for n=4 k=4
..3........2........0........2........3........0........0........3
..2.3......2.3......0.0......1.1......3.3......0.0......1.0......2.3
..3.2.2....2.2.2....1.0.0....2.1.1....2.3.3....0.1.0....0.0.1....3.3.4
..2.3.2.3..1.2.3.3..0.1.1.0..1.1.2.1..3.3.3.2..0.0.0.0..1.1.1.0..3.4.4.3
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CROSSREFS
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Sequence in context: A224665 A098514 A161198 * A093898 A194931 A195248
Adjacent sequences: A195229 A195230 A195231 * A195233 A195234 A195235
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Sep 13 2011
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STATUS
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approved
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