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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 (list; table; graph; refs; listen; history; text; internal format)
 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 R. H. Hardin, Table of n, a(n) for n = 1..205 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 Adjacent sequences: A195229 A195230 A195231 * A195233 A195234 A195235 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Sep 13 2011 STATUS approved

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Last modified March 26 23:26 EDT 2023. Contains 361553 sequences. (Running on oeis4.)