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A195279 Number of lower triangles of a 3 X 3 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once. 2

%I

%S 171,2125,11319,39609,107811,248261,507375,948209,1653019,2725821,

%T 4294951,6515625,9572499,13682229,19096031,26102241,35028875,46246189,

%U 60169239,77260441,98032131,123049125,152931279,188356049,230061051

%N Number of lower triangles of a 3 X 3 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

%C Row 3 of A195278.

%H R. H. Hardin, <a href="/A195279/b195279.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (64/3)*n^5 + (160/3)*n^4 + 56*n^3 + (92/3)*n^2 + (26/3)*n + 1.

%F Conjectures from _Colin Barker_, Mar 01 2018: (Start)

%F G.f.: x*(171 + 1099*x + 1134*x^2 + 150*x^3 + 7*x^4 - x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=5:

%e ...0.........0.........0.........0.........0.........0.........0.........0

%e ..-2.-1......3..4.....-3..1.....-4.-1.....-1..4.....-5.-1......5..8......4..4

%e ..-3.-6.-6...2..1..1..-7.-3..0..-5.-4.-6..-4.-1..3..-7.-2..2...8..5..2...0..0.-2

%Y Cf. A195278.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 14 2011

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Last modified August 10 16:03 EDT 2022. Contains 356039 sequences. (Running on oeis4.)