proposed

approved

editing

proposed

Empirical g.f.: 6*x*(30 + 29*x - 177*x^2 - 187*x^3 + 188*x^4 + 197*x^5 - 5*x^6 - 23*x^7) / ((1 - x - x^2)*(1 - 2*x - 11*x^2 + 14*x^4 + 2*x^5 - 2*x^6)). - Colin Barker, Jun 12 2018

Cf. A205823.

approved

editing

editing

approved

Number of (n+1)X4 X 4 0..2 arrays with the number of clockwise edge increases in every 2X2 2 X 2 subblock unequal to the number of anticlockwise counterclockwise edge increases.

Column 3 of A205823.

Empirical: a(n) = 3*a(n-1) + 10*a(n-2) - 13*a(n-3) - 25*a(n-4) + 12*a(n-5) + 18*a(n-6) - 2*a(n-8).

Some solutions for n=4:

R. H. Hardin , Feb 01 2012

approved

editing

_R. H. Hardin (rhhardin(AT)att.net) _ Feb 01 2012

editing

approved

R. H. Hardin, <a href="/A205818/b205818.txt">Table of n, a(n) for n = 1..210</a>

allocated for Ron HardinNumber of (n+1)X4 0..2 arrays with the number of clockwise edge increases in every 2X2 subblock unequal to the number of anticlockwise edge increases

180, 714, 2880, 12318, 53100, 230532, 1002240, 4361064, 18980472, 82617132, 359622708, 1565418528, 6814215036, 29662110636, 129118523304, 562050276348, 2446593518052, 10649972628456, 46359118343628, 201800318106108

1,1

Column 3 of A205823

Empirical: a(n) = 3*a(n-1) +10*a(n-2) -13*a(n-3) -25*a(n-4) +12*a(n-5) +18*a(n-6) -2*a(n-8)

Some solutions for n=4

..1..0..0..2....0..0..2..2....2..2..2..0....1..1..1..0....1..2..1..1

..1..2..1..2....2..1..1..0....1..0..1..0....2..0..2..2....1..0..0..2

..1..0..1..0....2..0..2..2....1..2..1..2....2..1..1..0....2..2..1..1

..2..0..2..2....1..1..1..0....0..2..0..2....2..0..2..2....1..0..0..2

..2..1..1..0....2..0..2..0....0..1..1..1....2..1..1..0....1..2..1..2

allocated

nonn

R. H. Hardin (rhhardin(AT)att.net) Feb 01 2012

approved

editing

allocated for Ron Hardin

allocated

approved