A205186 - OEIS

A205186

Number of (n+1) X (n+1) 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

%I #11 Jan 19 2018 05:11:36

%S 16,40,124,256,736,1408,3904,7168,19456,34816,93184,163840,434176,

%T 753664,1982464,3407872,8912896,15204352,39583744,67108864,174063616,

%U 293601280,759169024,1275068416,3288334336

%N Number of (n+1) X (n+1) 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

%C Diagonal of A205193.

%F Conjectures from _Colin Barker_, Jan 17 2018: (Start)

%F G.f.: 4*x*(4 + 10*x - x^2 - 16*x^3) / ((1 - 2*x)^2*(1 + 2*x)^2).

%F a(n) = 8*a(n-2) - 16*a(n-4) for n>3.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 23 2012