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A216797 Number of permutations of an n X 5 array with each element moving exactly one horizontally or vertically and without 2-loops.

%I A216797 #8 Mar 09 2018 10:44:25
%S A216797 0,10,0,292,0,10140,0,361200,0,12911864,0,461788640,0,16516859104,0,
%T A216797 590766585904,0,21130267285488,0,755777826856944,0,27032319708816080,
%U A216797 0,966879797484085808,0,34582919761038885136,0,1236946249622251150000,0
%N A216797 Number of permutations of an n X 5 array with each element moving exactly one horizontally or vertically and without 2-loops.
%C A216797 Column 5 of A216800.
%H A216797 R. H. Hardin, <a href="/A216797/b216797.txt">Table of n, a(n) for n = 1..210</a>
%F A216797 Empirical: a(n) = 49*a(n-2) - 524*a(n-4) + 1862*a(n-6) - 1728*a(n-8).
%F A216797 Empirical g.f.: 2*x^2*(5 - 99*x^2 + 536*x^4 - 636*x^6) / (1 - 49*x^2 + 524*x^4 - 1862*x^6 + 1728*x^8). - _Colin Barker_, Mar 09 2018
%e A216797 Some solutions for n=4:
%e A216797 ..1..2..7..8..3....5..0..1..4..9....5..0..3..4..9....1..6..7..2..3
%e A216797 ..0..5..6..9..4...10..7..2..3.14....6..1..2.13..8....0..5..8..9..4
%e A216797 .11.12.13.14.19...15..6.13..8.19...11.12..7.14.19...15.10.11.14.19
%e A216797 .10.15.16.17.18...16.11.12.17.18...10.15.16.17.18...16.17.12.13.18
%Y A216797 Cf. A216800.
%K A216797 nonn
%O A216797 1,2
%A A216797 _R. H. Hardin_, Sep 17 2012