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%I #4 Nov 20 2015 06:59:22
%S 0,1,1,0,2,0,0,4,4,0,1,9,4,9,1,0,18,22,22,18,0,0,41,65,112,65,41,0,1,
%T 84,193,716,716,193,84,1,0,176,628,3100,6656,3100,628,176,0,0,369,
%U 1905,14871,48781,48781,14871,1905,369,0,1,772,5929,73900,406871,580796
%N T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 1,1 2,2 -1,0 or 0,-1.
%C Table starts
%C .0...1.....0.......0.........1...........0.............0..............1
%C .1...2.....4.......9........18..........41............84............176
%C .0...4.....4......22........65.........193...........628...........1905
%C .0...9....22.....112.......716........3100.........14871..........73900
%C .1..18....65.....716......6656.......48781........406871........3133028
%C .0..41...193....3100.....48781......580796.......7644038.......93971260
%C .0..84...628...14871....406871.....7644038.....159104356.....3198623964
%C .1.176..1905...73900...3133028....93971260....3198623964...100746278612
%C .0.369..5929..349328..24130345..1163775908...62394318265..3118543214377
%C .0.772.18406.1679736.189393503.14482108589.1226341881232.98267901838019
%H R. H. Hardin, <a href="/A264655/b264655.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-3)
%F k=2: a(n) = 2*a(n-1) +2*a(n-5) -2*a(n-6) +4*a(n-7) -a(n-10)
%F k=3: [order 15]
%F k=4: [order 18] for n>21
%e Some solutions for n=4 k=4
%e ..1..6..7..4..9....1..2..3..4..9....5..2..3..4..9....1..2..7..4..9
%e .10.11..8..2..3...10..7..8.13.14...10..0..1.13.14....6.11.12.13..3
%e .15.16..0.14.19...15.16..0.18.19...11.16..6.18..8...15.16..0.14..8
%e .20.17..5.12.13...20.17..5..6.24...20.17.22.19..7...20.10..5.19.24
%e .21.22.23.24.18...21.22.23.11.12...21.15.23.24.12...21.22.23.17.18
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Nov 20 2015
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