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

1,1

Comments

Diagonal of A205193.

Links

Table of n, a(n) for n=1..25.

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)

Example

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

Crossrefs

Sequence in context: A185790 A185761 A205248 * A197903 A300901 A174086

Adjacent sequences: A205183 A205184 A205185 * A205187 A205188 A205189

Keyword

nonn

Author

R. H. Hardin, Jan 23 2012

Status

approved