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%I #11 Jan 06 2019 07:08:08
%S 17,96,596,3610,21997,133836,814609,4957760,30173957,183643896,
%T 1117690025,6802461466,41401001380,251973919068,1533558468205,
%U 9333511899338,56805427515893,345728020681728,2104162744903661
%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 -1,0 or 0,-2.
%H R. H. Hardin, <a href="/A264211/b264211.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) + 3*a(n-2) - 16*a(n-3) + 3*a(n-4) + 16*a(n-5) + 3*a(n-6) - 6*a(n-7) - a(n-8).
%F Empirical g.f.: x*(17 - 6*x - 31*x^2 + 18*x^3 + 34*x^4 - 13*x^6 - 2*x^7) / (1 - 6*x - 3*x^2 + 16*x^3 - 3*x^4 - 16*x^5 - 3*x^6 + 6*x^7 + x^8). - _Colin Barker_, Jan 06 2019
%e Some solutions for n=4:
%e ..0..1..2....0..4..1....2..0..1....0..4..2....2..0..1....3..4..2....0..1..2
%e ..5..7..4....5..3..2....6..7..8....3..1..5....5..3..4....0..1..5....6..4..5
%e ..3..6..8....9..6..7....3..4..5....8..7.11....8..6..7....9..7..8....3..7.11
%e .12.13.11...12.10..8....9.10.11....6.13.10...12..9.10....6.13.10...12.10..8
%e ..9.10.14...14.13.11...12.13.14....9.12.14...14.13.11...14.12.11....9.13.14
%Y Column 2 of A264217.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 08 2015