%I #8 Mar 21 2018 06:55:14

%S 6,20,68,240,832,2896,10080,35072,122048,424704,1477888,5142784,

%T 17895936,62274560,216704000,754089984,2624094208,9131364352,

%U 31775465472,110572765184,384772849664,1338938621952,4659259703296,16213365293056

%N Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,1 1,0 -1,-2 or 0,2.

%C Column 2 of A264313.

%H R. H. Hardin, <a href="/A264307/b264307.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 4*a(n-3).

%F Empirical g.f.: 2*x*(3 + 4*x + 2*x^2) / (1 - 2*x - 4*x^2 - 4*x^3). - _Colin Barker_, Mar 21 2018

%e Some solutions for n=4:

%e ..0..1..2....0..1..2....5..1..0....5..1..0....5..1..0....5..0..2....5..1..0

%e ..8..4..3....3..4..5....8..4..2....3..4..2....3..4..2....8..1..4....8..3..2

%e .11..6..5....6..7..8....3..7..6...11..6..8...11..6..7....3..6..7...11..4..6

%e .14..7.10....9.10.11...14.10.11....9..7.10...14.10..8...14.10.11...14..7.10

%e ..9.13.12...12.13.14....9.12.13...12.13.14....9.12.13....9.12.13....9.12.13

%Y Cf. A264313.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2015