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%I #8 May 02 2018 08:49:16
%S 5,61,666,7300,80282,883049,9712873,106834338,1175098084,12925203122,
%T 142167601085,1563737653381,17199948722346,189186616701220,
%U 2080911781577162,22888478678939969,251756206521753553
%N Number of n X 4 array permutations with each element moving zero or one space horizontally or diagonally.
%C Column 4 of A189449.
%H R. H. Hardin, <a href="/A189444/b189444.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 12*a(n-1) -12*a(n-2) +12*a(n-3) -12*a(n-4) +a(n-5).
%F Empirical g.f.: x*(5 + x - 6*x^2 - 20*x^3 + 2*x^4) / ((1 - x)*(1 - 11*x + x^2 - 11*x^3 + x^4)). - _Colin Barker_, May 02 2018
%e Some solutions for 3 X 4:
%e ..0..1..3..2....1..0..2..3....5..1..2..3....5..1..3..2....0..6..2..3
%e ..4..5..7..6....9.10.11..7....9..0..7..6....4..0..7..6....9..4..1..7
%e ..9..8.11.10....8..4..5..6....8..4.11.10....8..9.11.10....8.10..5.11
%Y Cf. A189449.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 22 2011