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A195232
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
12
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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
CROSSREFS
Sequence in context: A224665 A098514 A161198 * A093898 A194931 A195248
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 13 2011
STATUS
approved