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

1,2

Comments

Row 2 of A221828.

Links

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

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)

Example

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

Crossrefs

Cf. A221828.

Sequence in context: A037098 A316170 A038602 * A004303 A335625 A317365

Adjacent sequences: A221826 A221827 A221828 * A221830 A221831 A221832

Keyword

nonn

Author

R. H. Hardin, Jan 26 2013

Status

approved