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%I #8 Feb 23 2018 11:53:18
%S 0,6,8,88,292,1774,7676,39844,186996,927134,4460016,21812696,
%T 105716132,514912230,2501152692,12167375908,59142175940,287602784246,
%U 1398239939960,6798750327544,33055539575012,160722650037822,781448253270316
%N Number of permutations of an n X 4 array with each element moving exactly one horizontally or vertically and without 2-loops.
%C Column 4 of A216800.
%H R. H. Hardin, <a href="/A216796/b216796.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +10*a(n-2) -28*a(n-3) -7*a(n-4) +30*a(n-5) -8*a(n-6).
%F Empirical g.f.: 2*x^2*(1 - 2*x)*(3 - 2*x - 6*x^2 + 2*x^3) / ((1 - x)*(1 - 3*x - 13*x^2 + 15*x^3 + 22*x^4 - 8*x^5)). - _Colin Barker_, Feb 23 2018
%e Some solutions for n=4:
%e ..4..0..3..7....4..0..3..7....1..2..3..7....1..5..3..7....4..0..1..2
%e ..5..1..2.11....5..1..2.11....0..9..5..6....0..4..2.11....8..6..7..3
%e .12..8..6.15....9.13..6.15....4.10.11.15....9.10..6.15...12..5.11.15
%e .13..9.10.14....8.12.10.14....8.12.13.14....8.12.13.14...13..9.10.14
%Y Cf. A216800.
%K nonn
%O 1,2
%A _R. H. Hardin_, Sep 17 2012
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