A221731 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns.

3, 17, 91, 489, 2627, 14113, 75819, 407321, 2188243, 11755857, 63155771, 339290569, 1822764387, 9792403073, 52607544139, 282622526841, 1518327722483, 8156883666097, 43821073775451, 235419136209449, 1264737828598147

Offset

1,1

Comments

Column 2 of A221736.

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).

Conjectures from Colin Barker, Mar 14 2018: (Start)

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

a(n) = (2^(-1-n)*((5-sqrt(33))^n*(-1+sqrt(33)) + (1+sqrt(33))*(5+sqrt(33))^n)) / sqrt(33).

(End)

Example

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

Crossrefs

Cf. A221736.

Sequence in context: A198766 A240652 A204092 * A290925 A020056 A086842

Adjacent sequences: A221728 A221729 A221730 * A221732 A221733 A221734

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved