%I #5 Nov 10 2015 12:39:24
%S 4,16,16,96,256,96,256,1296,1296,256,5632,28561,67600,28561,5632,9216,
%T 331776,313600,313600,331776,9216,184320,4100625,273566336,106172416,
%U 273566336,4100625,184320,262144,49787136,830361856
%N T(n,k)=Number of (n+2)X(k+2) arrays of permutations of 0..(n+2)*(k+2)-1 with each element moved 0 or 1 knight moves and no more than 1 element left unmoved.
%C Table starts
%C ......4......16........96.......256......5632......9216...184320.262144
%C .....16.....256......1296.....28561....331776...4100625.49787136
%C .....96....1296.....67600....313600.273566336.830361856
%C ....256...28561....313600.106172416
%C ...5632..331776.273566336
%C ...9216.4100625
%C .184320
%F Empirical for column k:
%F k=1: [linear recurrence of order 60]
%F k=2: [order 41]
%e Some solutions for n=3 k=4
%e ..8.14..6..7.17..9....8.12.13.11.17..9....8.14.15.16.17..9....8.12.15.11.17..9
%e .19..3..0..5..2.22...19.18..0..5.14..3....2.18..4..5.23..3...14..3..4..5..2.22
%e ..1.24.10.23.29..4....1..2.25.28.29..4....1..0.25.11.27.28....1..0.25.23.27.28
%e .26.27.28.25.11.15....7..6.24.10.26.27....7..6.24.29.26.10....7..6.24.29.26.10
%e .13.12.18.16.20.21...20.21.22.23.15.16...13.12.22.19.20.21...13.21.18.19.20.16
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Oct 21 2015