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.
16, 40, 124, 256, 736, 1408, 3904, 7168, 19456, 34816, 93184, 163840, 434176, 753664, 1982464, 3407872, 8912896, 15204352, 39583744, 67108864, 174063616, 293601280, 759169024, 1275068416, 3288334336
Offset: 1
Keywords
Examples
Some solutions for n=4: 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0
Formula
Conjectures from Colin Barker, Jan 17 2018: (Start)
G.f.: 4*x*(4 + 10*x - x^2 - 16*x^3) / ((1 - 2*x)^2*(1 + 2*x)^2).
a(n) = 8*a(n-2) - 16*a(n-4) for n>3.
(End)
Comments