A206200 - OEIS

%I #10 Jun 14 2018 08:18:52

%S 480,1060,3008,9464,22576,67968,192808,496088,1475768,4018720,

%T 10894120,31512000,85274000,237162184,670298216,1827175160,5121768064,

%U 14281894072,39288809968,110061644032,305182278280,845001830872,2359774258680

%N Number of (n+1) X 3 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly one clockwise edge increases.

%C Column 2 of A206206.

%H R. H. Hardin, <a href="/A206200/b206200.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-2) + 14*a(n-3) - 3*a(n-4) + a(n-5) + a(n-6) + a(n-7) for n > 9.

%F Empirical g.f.: 4*x*(120 + 265*x + 392*x^2 - 109*x^3 + 38*x^4 + 41*x^5 + 17*x^6 - 9*x^7 - 3*x^8) / (1 - 3*x^2 - 14*x^3 + 3*x^4 - x^5 - x^6 - x^7). - _Colin Barker_, Jun 14 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A206206.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2012