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A211911 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, vertical, diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.

%I A211911 #9 Jul 20 2018 09:36:57
%S A211911 0,1,6,25,70,156,301,526,855,1315,1936,2751,3796,5110,6735,8716,11101,
%T A211911 13941,17290,21205,25746,30976,36961,43770,51475,60151,69876,80731,
%U A211911 92800,106170,120931,137176,155001,174505,195790,218961,244126,271396,300885
%N A211911 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, vertical, diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.
%C A211911 Column 1 of A211916.
%H A211911 R. H. Hardin, <a href="/A211911/b211911.txt">Table of n, a(n) for n = 1..74</a>
%F A211911 Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (17/8)*n^2 + (11/4)*n for n>1.
%F A211911 Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F A211911 G.f.: x^2*(1 + x + 5*x^2 - 5*x^3 + x^4) / (1 - x)^5.
%F A211911 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F A211911 (End)
%e A211911 Some solutions for n=4:
%e A211911 ..0........0........0........0........0........0........0........0
%e A211911 ..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
%e A211911 ..3.4.5....3.4.5....3.4.5....3.4.5....3.4.5....3.4.5....3.4.1....3.4.5
%e A211911 ..0.6.7.8..6.7.8.1..1.6.7.8..6.7.3.8..6.7.8.7..6.1.7.8..5.6.7.8..6.7.8.3
%Y A211911 Cf. A211916.
%K A211911 nonn
%O A211911 1,3
%A A211911 _R. H. Hardin_, Apr 25 2012