A233637 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 2.

24, 90, 324, 1188, 4320, 15768, 57456, 209520, 763776, 2784672, 10152000, 37012032, 134936064, 491944320, 1793505024, 6538675968, 23838382080, 86908819968, 316847932416, 1155148784640, 4211385163776, 15353663035392, 55975637053440

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2).

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

G.f.: 6*x*(4 + 7*x) / (1 - 2*x - 6*x^2).

a(n) = ((1-sqrt(7))^n*(-17+7*sqrt(7)) + (1+sqrt(7))^n*(17+7*sqrt(7))) / (2*sqrt(7)).

(End)

Example

Some solutions for n=5:
..1..1....1..2....0..1....0..0....1..1....1..0....0..1....1..0....2..2....0..1
..1..2....1..2....0..1....1..0....2..1....1..1....1..1....1..0....2..1....0..1
..1..2....1..2....1..1....1..0....2..1....0..1....0..0....1..1....1..1....0..1
..2..2....2..2....0..1....1..0....2..1....1..1....1..0....2..1....0..1....1..1
..1..1....1..1....1..1....1..0....1..1....0..1....1..1....1..1....1..1....1..0
..2..1....0..0....0..1....1..1....0..0....0..0....0..1....2..2....1..2....1..0

Crossrefs

Column 1 of A233644.

Sequence in context: A233644 A010012 A256718 * A179962 A076799 A297540

Adjacent sequences: A233634 A233635 A233636 * A233638 A233639 A233640

Keyword

nonn

Author

R. H. Hardin, Dec 14 2013

Status

approved