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A211905 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal or vertical neighbor, and containing the value n(n+1)/2-2. 2

%I #9 May 22 2014 03:34:45

%S 0,2,10,34,86,181,337,575,919,1396,2036,2872,3940,5279,6931,8941,

%T 11357,14230,17614,21566,26146,31417,37445,44299,52051,60776,70552,

%U 81460,93584,107011,121831,138137,156025,175594,196946,220186,245422,272765,302329

%N Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal or vertical neighbor, and containing the value n(n+1)/2-2.

%C Column 1 of A211910.

%H R. H. Hardin, <a href="/A211905/b211905.txt">Table of n, a(n) for n = 1..76</a>

%F Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (9/8)*n^2 + (3/4)*n + 1 for n>1.

%e Some solutions for n=4:

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

%e ..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2

%e ..3.4.5....3.4.5....3.0.4....3.4.5....3.4.5....3.4.3....3.4.5....3.4.5

%e ..6.0.7.8..6.7.8.7..5.6.7.8..6.7.4.8..6.7.8.4..5.6.7.8..6.1.7.8..6.7.0.8

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 25 2012

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