%I #9 Feb 26 2018 12:14:51
%S 37,285,1012,2467,4708,7748,11588,16228,21668,27908,34948,42788,51428,
%T 60868,71108,82148,93988,106628,120068,134308,149348,165188,181828,
%U 199268,217508,236548,256388,277028,298468,320708,343748,367588,392228
%N Number of slanted n X 4 (i=1..n) X (j=i..4+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 3 neighbors with the same value.
%C Same recurrence for A165392.
%H R. H. Hardin, <a href="/A165381/b165381.txt">Table of n, a(n) for n=2..99</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=9.
%F Conjectures from _Colin Barker_, Feb 26 2018: (Start)
%F G.f.: x^2*(37 + 174*x + 268*x^2 + 249*x^3 + 58*x^4 + 13*x^5 + x^6) / (1 - x)^3.
%F a(n) = 4*(817 - 540*n + 100*n^2) for n>5.
%F (End)
%e Some solutions for n=3:
%e ...1.3.2.2.......1.1.3.2.......1.1.1.2.......1.1.2.2.......1.1.2.2....
%e .....3.3.2.2.......3.3.2.2.......1.4.4.4.......1.2.2.2.......1.3.2.2..
%e .......3.3.3.4.......3.3.3.4.......3.4.4.4.......3.3.3.4.......3.2.2.4
%e ------
%e ...1.1.2.2.......1.1.2.2.......1.1.1.2.......1.1.2.2.......1.1.1.2....
%e .....1.1.1.4.......2.2.2.4.......2.2.2.4.......2.2.4.4.......1.1.2.4..
%e .......3.1.4.4.......3.4.4.4.......3.4.4.4.......3.4.4.4.......3.3.4.4
%Y Cf. A165392.
%K nonn
%O 2,1
%A _R. H. Hardin_, Sep 17 2009