A221788 - OEIS

A221788

Number of 3 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without 2-loops or left turns.

%I #8 Aug 10 2018 17:34:26

%S 0,0,0,5,24,142,840,4919,28704,167344,975408,5685161,33135624,

%T 193128658,1125636408,6560689883,38238502992,222870328180,

%U 1298983466208,7571030469197,44127199349112,257192165625622,1499025794404776

%N Number of 3 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without 2-loops or left turns.

%C Row 3 of A221787.

%H R. H. Hardin, <a href="/A221788/b221788.txt">Table of n, a(n) for n = 1..85</a>

%F Empirical: a(n) = 8*a(n-1) - 14*a(n-2) + 8*a(n-3) - a(n-4) for n>6.

%F Conjectures from _Colin Barker_, Aug 10 2018: (Start)

%F G.f.: x^4*(5 - 16*x + 20*x^2) / ((1 - x)^2*(1 - 6*x + x^2)).

%F a(n) = (408 + sqrt(2)*((10041-7100*sqrt(2))*(3+2*sqrt(2))^n - (3-2*sqrt(2))^n*(10041+7100*sqrt(2))) - 72*(1+n)) / 32 for n>2.

%F (End)

%Y Cf. A221787.

%K nonn

%O 1,4

%A _R. H. Hardin_, Jan 25 2013