A205065 Number of (n+1) X 2 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock differing from the number in all its horizontal and vertical neighbors.

16, 40, 98, 238, 584, 1432, 3516, 8622, 21158, 51894, 127322, 312310, 766198, 1879520, 4610912, 11311058, 27748262, 68070236, 166988412, 409647388, 1004934200, 2465259322, 6047686542, 14835930358, 36394946602, 89282603930

Offset

1,1

Comments

Column 1 of A205072.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-2) + 2*a(n-3) + 4*a(n-5) - 3*a(n-6) + 4*a(n-8) - 2*a(n-9) for n > 10.

Empirical g.f.: 2*x*(8 + 20*x + 9*x^2 + 3*x^3 + 7*x^4 - 9*x^5 + 4*x^6 + 11*x^7 - 4*x^8 + x^9) / (1 - 5*x^2 - 2*x^3 - 4*x^5 + 3*x^6 - 4*x^8 + 2*x^9). - Colin Barker, Jun 10 2018

Example

Some solutions for n=4:
 1 0   0 1   0 1   1 1   1 1   0 0   1 0   0 0   1 1   0 0
 0 1   0 0   1 1   1 1   0 1   1 0   0 0   0 1   1 1   0 1
 0 0   1 1   0 1   0 1   0 1   0 1   0 1   0 0   0 1   0 0
 0 1   1 1   0 1   0 1   0 0   0 0   0 0   0 1   1 1   0 0
 0 0   0 1   0 0   0 0   1 1   1 1   0 1   0 0   1 1   0 1

Crossrefs

Cf. A205072.

Sequence in context: A184030 A350284 A182461 * A368078 A185790 A185761

Adjacent sequences: A205062 A205063 A205064 * A205066 A205067 A205068

Keyword

nonn

Author

R. H. Hardin, Jan 21 2012

Status

approved