A212031 - OEIS

%I #10 Jul 20 2018 14:36:04

%S 0,3,10,31,78,166,313,540,871,1333,1956,2773,3820,5136,6763,8746,

%T 11133,13975,17326,21243,25786,31018,37005,43816,51523,60201,69928,

%U 80785,92856,106228,120991,137238,155065,174571,195858,219031,244198,271470,300961

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

%C Column 1 of A212036.

%H R. H. Hardin, <a href="/A212031/b212031.txt">Table of n, a(n) for n = 1..70</a>

%F Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (17/8)*n^2 + (19/4)*n - 2 for n>1.

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

%F G.f.: x^2*(3 - 5*x + 11*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......1.1......1.2......1.2

%e ..1.3.4....3.2.4....3.4.5....3.4.5....3.0.4....2.3.4....3.4.5....3.4.1

%e ..5.6.7.8..5.6.7.8..6.7.3.8..6.7.8.6..5.6.7.8..5.6.7.8..5.6.7.8..5.6.7.8

%Y Cf. A212036.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 27 2012