A234259 - OEIS

%I #13 Jun 20 2022 21:34:03

%S 20,46,104,244,560,1336,3104,7504,17600,42976,101504,249664,592640,

%T 1465216,3490304,8660224,20679680,51437056,123029504,306525184,

%U 733982720,1830762496,4387119104,10951020544,26255605760,65571905536,157265199104

%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234259/b234259.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - 12*a(n-3).

%F Conjectures from _Colin Barker_, Oct 14 2018: (Start)

%F G.f.: 2*x*(10 + 3*x - 54*x^2) / ((1 - 2*x)*(1 - 6*x^2)).

%F a(n) = 2^(2+n) + 2^((-3+n)/2)*3^((-1+n)/2)*(12-12*(-1)^n+5*sqrt(6)+5*(-1)^n*sqrt(6)).

%F (End)

%e Some solutions for n=5:

%e   0 2   0 0   0 2   2 0   0 0   2 0   0 2   2 0   0 2   0 2

%e   2 2   2 0   1 1   2 2   0 2   2 2   0 0   2 2   2 2   2 2

%e   0 2   2 2   2 0   0 2   0 0   2 0   2 0   2 0   2 0   2 0

%e   0 0   0 2   0 0   2 2   0 2   2 2   1 1   1 1   2 2   1 1

%e   2 0   1 1   2 0   0 2   2 2   0 2   2 0   2 0   0 2   2 0

%e   2 2   0 2   0 0   2 2   2 0   1 1   1 1   1 1   1 1   0 0

%Y Column 1 of A234266.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 22 2013