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 A195233 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less. 1

%I #9 May 06 2018 11:53:12

%S 64,155,246,337,428,519,610,701,792,883,974,1065,1156,1247,1338,1429,

%T 1520,1611,1702,1793,1884,1975,2066,2157,2248,2339,2430,2521,2612,

%U 2703,2794,2885,2976,3067,3158,3249,3340,3431,3522,3613,3704,3795,3886,3977

%N Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

%C Row 3 of A195232.

%H R. H. Hardin, <a href="/A195233/b195233.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 91*n - 27.

%F Conjectures from _Colin Barker_, May 06 2018: (Start)

%F G.f.: x*(64 + 27*x) / (1 - x)^2.

%F a(n) = 2*a(n-1) - a(n-2) for n>2.

%F (End)

%e Some solutions for n=4:

%e ..2......1......0......2......1......3......2......0......4......3......0

%e ..2.3....2.1....0.1....1.1....0.0....2.2....2.1....0.1....3.3....4.3....0.0

%e ..2.3.3..1.1.2..0.1.1..2.2.1..0.0.0..2.2.1..2.1.1..1.0.0..3.4.4..3.3.4..0.1.1

%Y Cf. A195232.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 13 2011

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Last modified June 10 05:41 EDT 2023. Contains 363195 sequences. (Running on oeis4.)