A216985 Number of city-block distance 1, pressure limit 2 movements in an n X 2 array with each element moving exactly one horizontally or vertically, no element acquiring more than two neighbors, and without 2-loops.

0, 2, 14, 80, 436, 2346, 12578, 67368, 360720, 1931306, 10340030, 55359176, 296385268, 1586804322, 8495522018, 45483800496, 243513709632, 1303737284978, 6980021408654, 37370028005408, 200073740644948, 1071165953874618

Offset

1,2

Comments

Column 2 of A216991.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 9*a(n-2) + a(n-3).

Empirical g.f.: 2*x^2 / (1 - 7*x + 9*x^2 - x^3). - Colin Barker, Jul 23 2018

Example

Some solutions for n=3 (movement: 0=n 1=e 2=s 3=w):
..2..2....2..2....1..2....2..3....2..3....1..2....1..2....1..2....2..3....2..3
..1..2....2..3....1..2....1..0....1..0....0..3....0..2....0..3....1..2....2..0
..0..3....1..0....0..3....1..0....0..3....0..0....0..3....1..0....0..3....1..0

Crossrefs

Cf. A216991.

Sequence in context: A112408 A026291 A220867 * A361813 A102401 A077461

Adjacent sequences: A216982 A216983 A216984 * A216986 A216987 A216988

Keyword

nonn

Author

R. H. Hardin, Sep 21 2012

Status

approved