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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 or antidiagonal neighbor, and containing the value n(n+1)/2-3
0

%I #4 Dec 18 2015 18:18:09

%S 0,2,23,340,2577,12616,46582,141478,372360,878257,1899356,3828287,

%T 7278658,13174305,22863037,38258971,62017867,97750188,150276925,

%U 225933542,332927711,481756822,685691568

%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, vertical or antidiagonal neighbor, and containing the value n(n+1)/2-3

%C Column 2 of A211930

%F Empirical: a(n) = (1/128)*n^8 + (1/32)*n^7 - (41/192)*n^6 - (1/4)*n^5 + (345/128)*n^4 - (367/96)*n^3 - (143/96)*n^2 + (169/24)*n - 3 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......1.0......1.2......1.2......1.2

%e ..3.1.4....3.4.5....3.4.2....3.4.5....2.3.4....3.4.5....3.1.4....3.4.2

%e ..5.6.1.7..6.2.7.6..5.0.6.7..2.6.7.8..5.6.0.7..6.2.7.4..5.6.7.2..5.3.6.7

%K nonn

%O 1,2

%A _R. H. Hardin_ Apr 25 2012