A205919 - OEIS

A205919

Number of (n+1) X 2 0..3 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to one, and every 2 X 2 determinant nonzero.

%I #9 Jun 13 2018 05:43:09

%S 76,389,1828,9144,43572,215294,1035724,5082472,24576282,120140890,

%T 582580746,2841986300,13802576730,67255368928,326915006288,

%U 1591943059154,7741739157470,37686051760598,183317203390912,892200827543090

%N Number of (n+1) X 2 0..3 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to one, and every 2 X 2 determinant nonzero.

%C Column 1 of A205926.

%H R. H. Hardin, <a href="/A205919/b205919.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 18*a(n-2) + 3*a(n-3) - 2*a(n-4) + 26*a(n-5) + 28*a(n-6) + 8*a(n-7).

%F Empirical g.f.: x*(76 + 313*x + 71*x^2 + 86*x^3 + 509*x^4 + 448*x^5 + 116*x^6) / (1 - x - 18*x^2 - 3*x^3 + 2*x^4 - 26*x^5 - 28*x^6 - 8*x^7). - _Colin Barker_, Jun 13 2018

%e Some solutions for n=4:

%e ..3..2....2..1....3..1....0..1....3..0....3..1....0..1....0..3....1..1....3..1

%e ..3..0....2..2....1..1....1..1....3..3....1..1....1..1....1..1....3..0....3..3

%e ..3..3....1..2....0..1....0..1....3..1....0..1....2..1....1..2....3..3....3..0

%e ..2..3....2..2....1..1....1..1....1..1....1..1....1..1....1..1....2..3....3..3

%e ..2..2....3..0....0..1....2..0....3..0....3..0....2..0....0..1....2..2....1..2

%Y Cf. A205926.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 01 2012