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%I #6 Nov 10 2015 12:38:08
%S 16,256,1296,28561,331776,4100625,49787136,655360000,8100000000,
%T 101904600625,1281641353216,16160601000625,202865213941776,
%U 2552640623984896,32107262791520016,403852218590929761
%N Number of (n+2)X(2+2) arrays of permutations of 0..n*4+7 with each element moved 0 or 1 knight moves and no more than 1 element left unmoved.
%C Column 2 of A263568.
%H R. H. Hardin, <a href="/A263566/b263566.txt">Table of n, a(n) for n = 1..96</a>
%F Empirical: a(n) = 5*a(n-1) +51*a(n-2) +369*a(n-3) +2931*a(n-4) -6607*a(n-5) -3490*a(n-6) +7362*a(n-7) -489366*a(n-8) -431514*a(n-9) +3977678*a(n-10) -10138510*a(n-11) +11574177*a(n-12) -8356653*a(n-13) -28046919*a(n-14) +111372795*a(n-15) -213047067*a(n-16) +72776559*a(n-17) -25967340*a(n-18) +15214476*a(n-19) -105060228*a(n-20) +105060228*a(n-21) -15214476*a(n-22) +25967340*a(n-23) -72776559*a(n-24) +213047067*a(n-25) -111372795*a(n-26) +28046919*a(n-27) +8356653*a(n-28) -11574177*a(n-29) +10138510*a(n-30) -3977678*a(n-31) +431514*a(n-32) +489366*a(n-33) -7362*a(n-34) +3490*a(n-35) +6607*a(n-36) -2931*a(n-37) -369*a(n-38) -51*a(n-39) -5*a(n-40) +a(n-41)
%e Some solutions for n=4
%e ..6..7.11.10....6..7..4.10....9..7..4..5....9..7.11.10....6..8..4..5
%e ..2.12..0..1....2..3..0..1....2..3..0..1....2..3.15..1...13.11..0..9
%e .14.15..3.13...17.16.19..5...17.15.19.13....6..0..4.13....1..7..3..2
%e ..5..4..8..9...18.11.23.22...21.11.23..6....5.20.23.17...10.19.23.22
%e .22.23.20.21....9..8.20.21...22..8.20.10...22..8.12.21...14.15.20.21
%e .18.19.16.17...13.12.15.14...18.12.16.14...18.19.16.14...18.12.16.17
%Y Cf. A263568.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 21 2015