cp's OEIS Frontend

A221853 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal, diagonal or antidiagonal neighbor, without consecutive moves in the same direction.

%I A221853 #8 Aug 11 2018 10:45:36
%S A221853 1,31,302,3437,37155,406612,4434129,48397883,528123314,5763315281,
%T A221853 62892896491,686329748776,7489683895265,81732408497079,
%U A221853 891918279715066,9733204380907645,106215187016111667,1159090627331995148
%N A221853 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal, diagonal or antidiagonal neighbor, without consecutive moves in the same direction.
%C A221853 Row 2 of A221852.
%H A221853 R. H. Hardin, <a href="/A221853/b221853.txt">Table of n, a(n) for n = 1..37</a>
%F A221853 Empirical: a(n) = 13*a(n-1) - 14*a(n-2) - 113*a(n-3) + 189*a(n-4) - 10*a(n-5) - 42*a(n-6) + 18*a(n-7) - 2*a(n-8).
%F A221853 Empirical g.f.: x*(1 + 18*x - 87*x^2 + 58*x^3 + 16*x^4 - 8*x^5 - 2*x^6) / (1 - 13*x + 14*x^2 + 113*x^3 - 189*x^4 + 10*x^5 + 42*x^6 - 18*x^7 + 2*x^8). - _Colin Barker_, Aug 11 2018
%e A221853 Some solutions for n=3:
%e A221853 ..3..2..1....2..0..2....0..2..1....0..0..1....2..0..0....2..1..1....0..2..0
%e A221853 ..0..0..0....1..0..1....0..3..0....1..2..2....1..3..0....0..0..2....3..0..1
%Y A221853 Cf. A221852.
%K A221853 nonn
%O A221853 1,2
%A A221853 _R. H. Hardin_, Jan 27 2013