A217022 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 and no element acquiring more than two neighbors.

1, 16, 121, 1024, 8464, 70225, 582169, 4826809, 40018276, 331786225, 2750792704, 22806436324, 189084955921, 1567676780761, 12997387725721, 107759513809984, 893418974713225, 7407211077304336, 61412145361267600, 509159460762351025

Offset

1,2

Comments

Column 2 of A217028.

It seems that all terms are squares. - Colin Barker, Mar 09 2018

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -3*a(n-2) -25*a(n-3) +9*a(n-4) +3*a(n-5) -a(n-6).

Empirical g.f.: x*(1 + 7*x - 20*x^2 + 8*x^3 + 2*x^4 - x^5) / ((1 - 9*x + 6*x^2 - x^3)*(1 - 3*x^2 - x^3)). - Colin Barker, Mar 09 2018

Example

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

Crossrefs

Cf. A217028.

Sequence in context: A294140 A014765 A081071 * A069658 A069667 A104265

Adjacent sequences: A217019 A217020 A217021 * A217023 A217024 A217025

Keyword

nonn

Author

R. H. Hardin, Sep 24 2012

Status

approved