cp's OEIS Frontend

A222015 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

%I A222015 #9 Aug 14 2018 21:03:34
%S A222015 3,27,188,1363,9838,70994,512456,3698699,26696370,192687348,
%T A222015 1390767557,10038200482,72453134112,522947981192,3774503253017,
%U A222015 27243388115499,196635728242591,1419265821803368,10243893573843252,73937773981558032
%N A222015 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.
%C A222015 Column 2 of A222020.
%H A222015 R. H. Hardin, <a href="/A222015/b222015.txt">Table of n, a(n) for n = 1..210</a>
%F A222015 Empirical: a(n) = 3*a(n-1) + 25*a(n-2) + 40*a(n-3) + a(n-4) - 42*a(n-5) - 20*a(n-6) + 10*a(n-7) + 4*a(n-8) - a(n-9).
%F A222015 Empirical g.f.: x*(1 + x)*(3 + 15*x + 17*x^2 - 13*x^3 - 21*x^4 + 5*x^5 + 5*x^6 - x^7) / (1 - 3*x - 25*x^2 - 40*x^3 - x^4 + 42*x^5 + 20*x^6 - 10*x^7 - 4*x^8 + x^9). - _Colin Barker_, Aug 14 2018
%e A222015 Some solutions for n=3:
%e A222015 ..3..0....0..2....0..1....1..0....0..2....0..2....2..1....1..1....2..1....2..1
%e A222015 ..1..0....1..2....2..0....0..4....0..3....0..1....0..0....1..3....0..0....0..1
%e A222015 ..2..0....0..1....2..1....1..0....1..0....2..1....2..1....0..0....0..3....1..1
%Y A222015 Cf. A222020.
%K A222015 nonn
%O A222015 1,1
%A A222015 _R. H. Hardin_, Feb 05 2013