A221415 - OEIS

A221415

Number of n X 4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with every occupancy equal to zero or two.

%I #10 Aug 05 2018 08:20:59

%S 4,29,226,1766,13794,107695,840673,6561928,51218473,399777826,

%T 3120396286,24355691434,190103915555,1483821378069,11581696324348,

%U 90398811127357,705591374468222,5507364322727938,42986724144662890,335525006918408343

%N Number of n X 4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with every occupancy equal to zero or two.

%H R. H. Hardin, <a href="/A221415/b221415.txt">Table of n, a(n) for n = 1..90</a>

%F Empirical: a(n) = 10*a(n-1) - 15*a(n-2) - 19*a(n-3) + 17*a(n-4) + 12*a(n-5) - a(n-6) + a(n-7).

%F Empirical g.f.: x*(4 - 11*x - 4*x^2 + 17*x^3 + 7*x^4 - 2*x^5 + x^6) / (1 - 10*x + 15*x^2 + 19*x^3 - 17*x^4 - 12*x^5 + x^6 - x^7). - _Colin Barker_, Aug 05 2018

%e Some solutions for n=3:

%e ..2..2..2..0....0..2..2..0....0..2..0..0....0..2..0..2....0..2..0..2

%e ..0..2..0..0....0..2..0..0....2..0..2..2....0..2..2..0....2..0..2..0

%e ..0..0..2..2....2..2..2..0....0..2..2..0....2..0..2..0....2..0..0..2

%Y Column 4 of A221419.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 15 2013