A211958 - OEIS

%I #10 Jul 20 2018 10:02:17

%S 0,3,12,37,90,186,343,582,927,1405,2046,2883,3952,5292,6945,8956,

%T 11373,14247,17632,21585,26166,31438,37467,44322,52075,60801,70578,

%U 81487,93612,107040,121861,138168,156057,175627,196980,220221,245458,272802,302367

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

%C Column 1 of A211963.

%H R. H. Hardin, <a href="/A211958/b211958.txt">Table of n, a(n) for n = 1..74</a>

%F Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (9/8)*n^2 + (7/4)*n for n>1.

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

%F G.f.: x^2*(3 - 3*x + 7*x^2 - 5*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......1.1......1.2......1.2......1.2

%e ..3.4.5....3.0.4....3.4.5....3.4.5....2.3.4....1.3.4....3.4.0....3.4.5

%e ..3.6.7.8..5.6.7.8..6.7.8.0..6.0.7.8..5.6.7.8..5.6.7.8..5.6.7.8..6.7.8.1

%Y Cf. A211963.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 26 2012