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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 June 20 12:54 EDT 2021. Contains 345164 sequences. (Running on oeis4.)