%I #10 Jul 20 2018 14:47:40

%S 0,1,4,19,58,136,271,484,799,1243,1846,2641,3664,4954,6553,8506,10861,

%T 13669,16984,20863,25366,30556,36499,43264,50923,59551,69226,80029,

%U 92044,105358,120061,136246,154009,173449,194668,217771,242866,270064,299479

%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 element within a city block distance of two, and containing the value n(n+1)/2-2.

%C Column 1 of A212044.

%H R. H. Hardin, <a href="/A212039/b212039.txt">Table of n, a(n) for n = 1..73</a>

%F Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (25/8)*n^2 + (23/4)*n - 2 for n>1.

%F Conjectures from _Colin Barker_, Jul 20 2018: (Start)

%F G.f.: x^2*(1 - x + 9*x^2 - 7*x^3 + x^4) / (1 - x)^5.

%F 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 (End)

%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....3.4.5....3.4.5....3.4.1....3.4.5....3.4.5....3.4.5

%e ..6.7.8.1..6.7.8.0..6.7.3.8..6.7.0.8..5.6.7.8..6.7.8.3..6.7.2.8..6.1.7.8

%Y Cf. A212044.

%K nonn

%O 1,3

%A _R. H. Hardin_, Apr 28 2012