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%I #12 Jun 29 2023 11:24:39
%S 8,81,720,7056,70560,705600,7056000,70560000,705600000,7056000000,
%T 70560000000,705600000000,7056000000000,70560000000000,
%U 705600000000000,7056000000000000,70560000000000000,705600000000000000
%N Number of (n+1) X (3+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,-1 or 2,2.
%H R. H. Hardin, <a href="/A264185/b264185.txt">Table of n, a(n) for n = 1..210</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).
%F Empirical: a(n) = 10*a(n-1) for n>4.
%F Conjectures from _Colin Barker_, Jan 05 2019: (Start)
%F G.f.: x*(8 + x - 90*x^2 - 144*x^3) / (1 - 10*x).
%F a(n) = 441*2^n * 5^(n-4) for n>3.
%F (End)
%e Some solutions for n=4:
%e ..0.11..2..6...10.11..2..3....0.11..2..6....0..1..2..6...10..4..2..3
%e ..1..5..3..7....4..8..6..7....1..5..3..7....4.15..3.10....1.15..6..7
%e .18..9.10.14...18.12..0..1....8.19.13.14....5.19..7.11...18..9..0.11
%e .12.16..4.15....9.16.14..5...12.10..4.18...12.13.17.18...12.13.17..5
%e .13.17..8.19...13.17.15.19...16.17.15..9...16.14..8..9...16.14..8.19
%Y Column 3 of A264190.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 06 2015
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