A209531 Half the number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.

33, 193, 1025, 6145, 32769, 196609, 1048577, 6291457, 33554433, 201326593, 1073741825, 6442450945, 34359738369, 206158430209, 1099511627777, 6597069766657, 35184372088833, 211106232532993, 1125899906842625

Offset

1,1

Comments

Column 4 of A209534.

Links

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

Formula

Empirical: a(n) = a(n-1) + 32*a(n-2) - 32*a(n-3).

Conjectures from Colin Barker, Jul 11 2018: (Start)

G.f.: x*(33 + 160*x - 224*x^2) / ((1 - x)*(1 - 32*x^2)).

a(n) = 3*2^((5*n)/2 + 1) + 1 for n even.

a(n) = 2^((5*(n + 1))/2) + 1 for n odd.

(End)

Example

Some solutions for n=4:
..0..1..2..1..2....0..2..0..2..0....1..0..1..2..1....0..1..2..1..2
..1..0..1..2..1....2..0..2..0..2....2..1..2..1..0....1..0..1..2..1
..2..1..0..1..2....0..2..0..2..0....1..2..1..2..1....2..1..2..1..2
..1..2..1..2..1....2..0..2..0..2....2..1..2..1..2....1..0..1..2..1
..0..1..0..1..2....0..2..0..2..0....1..0..1..2..1....2..1..2..1..2

Crossrefs

Cf. A209534.

Sequence in context: A046142 A135827 A189180 * A127870 A380069 A142993

Adjacent sequences: A209528 A209529 A209530 * A209532 A209533 A209534

Keyword

nonn

Author

R. H. Hardin, Mar 10 2012

Status

approved