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%I #7 Nov 10 2015 12:37:41
%S 4,16,96,256,5632,9216,184320,262144,7064576,7929856,241238016,
%T 239878144,8348401664,7223640064,281579094016,218515111936,
%U 9420583469056,6595610148864,311967317229568,199285849194496,10252542491492352
%N Number of (n+2)X(1+2) arrays of permutations of 0..n*3+5 with each element moved 0 or 1 knight moves and no more than 1 element left unmoved.
%C Column 1 of A263568.
%H R. H. Hardin, <a href="/A263565/b263565.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 56*a(n-2) -304*a(n-4) -23808*a(n-6) +205056*a(n-8) +4083712*a(n-10) -45379584*a(n-12) -291962880*a(n-14) +4959371264*a(n-16) +1621622784*a(n-18) -273540972544*a(n-20) +989604085760*a(n-22) +4824523341824*a(n-24) -35707955445760*a(n-26) -13298560925696*a(n-28) +595864435294208*a(n-30) -787400649342976*a(n-32) -5646919921565696*a(n-34) +14188166764298240*a(n-36) +31254717531160576*a(n-38) -123045246752784384*a(n-40) -85436451524706304*a(n-42) +627003102809030656*a(n-44) -24910535438893056*a(n-46) -1922474090933780480*a(n-48) +993043717835194368*a(n-50) +3233584532452016128*a(n-52) -3026418949592973312*a(n-54) -2017612633061982208*a(n-56) +3458764513820540928*a(n-58) -1152921504606846976*a(n-60)
%e Some solutions for n=4
%e ..7..8..3....5..6..3....5..6..3....5..8..3....5..6..7....5..6..3....5..8..7
%e ..2..9.10....2..9..0....2..9..0....2..9..0...10.11..0....2..9..0....2..9..0
%e .13..0..1....1.14.13...13.14..1...13.12..1...13..2..1....1.14.13....1.12.13
%e ..4..5.16...16.17..4....4.15.16....4.17.16...16..3..4....4.15.16....4..3.16
%e .17..6.15....7..8.15...17..8..7....7..6.15...17..8.15...17..8..7...17..6.15
%e .14.11.12...10.11.12...10.11.12...14.11.10...14..9.12...10.11.12...14.11.10
%Y Cf. A263568.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 21 2015