A221829 Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

0, 3, 16, 73, 333, 1519, 6929, 31607, 144177, 657671, 3000001, 13684663, 62423313, 284747239, 1298889569, 5924953367, 27026987697, 123285031751, 562371183361, 2565285853303, 11701686899793, 53377862792359, 243485940162209

Offset: 1

Author

R. H. Hardin, Jan 26 2013

Keywords

• nonn

Comments

Row 2 of A221828.

Examples

			Some solutions for n=3:
..1..1..0....0..2..0....0..2..1....0..2..1....1..1..1....0..2..2....1..1..0
..2..1..1....1..2..1....1..2..0....1..1..1....1..2..0....0..1..1....1..2..1
		

Links

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

Crossrefs

Cf. A221828.

Formula

Empirical: a(n) = 5*a(n-1) - 2*a(n-2) for n>4.

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

G.f.: x^2*(3 + x - x^2) / (1 - 5*x + 2*x^2).

a(n) = (2^(-4-n)*((5-sqrt(17))^n*(-7+sqrt(17)) + (5+sqrt(17))^n*(7+sqrt(17)))) / sqrt(17) for n>2.

(End)