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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.
2
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 24 2012
STATUS
approved