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A264628 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 -2,0 -1,0 0,-1 or 1,1.

%I A264628 #4 Nov 19 2015 06:56:53
%S A264628 0,1,1,0,2,2,0,4,4,1,1,9,13,8,1,0,16,40,22,16,4,0,37,125,108,61,32,6,
%T A264628 1,76,393,684,660,280,64,5,0,160,1200,2736,6107,4032,832,128,7,0,337,
%U A264628 3759,13556,37225,50353,19521,2373,256,15,1,704,11572,68972,349391,604916
%N A264628 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 -2,0 -1,0 0,-1 or 1,1.
%C A264628 Table starts
%C A264628 ..0...1.....0.......0.........1...........0.............0..............1
%C A264628 ..1...2.....4.......9........16..........37............76............160
%C A264628 ..2...4....13......40.......125.........393..........1200...........3759
%C A264628 ..1...8....22.....108.......684........2736.........13556..........68972
%C A264628 ..1..16....61.....660......6107.......37225........349391........2557552
%C A264628 ..4..32...280....4032.....50353......604916.......7907841.......93847752
%C A264628 ..6..64...832...19521....389512.....7201068.....145801320.....2894056084
%C A264628 ..5.128..2373...89469...2986345....81028312....2739867178....84594500932
%C A264628 ..7.256..7225..449550..23242594...992539392...54011094032..2549159514025
%C A264628 .15.512.24371.2308554.180618759.12531858912.1041910674136.78013734570966
%H A264628 R. H. Hardin, <a href="/A264628/b264628.txt">Table of n, a(n) for n = 1..162</a>
%F A264628 Empirical for column k:
%F A264628 k=1: a(n) = a(n-3) +2*a(n-4) +a(n-5)
%F A264628 k=2: a(n) = 2*a(n-1)
%F A264628 k=3: [order 45]
%F A264628 k=4: [order 11] for n>12
%F A264628 Empirical for row n:
%F A264628 n=1: a(n) = a(n-3)
%F A264628 n=2: a(n) = 2*a(n-1) +2*a(n-5) -2*a(n-6) +4*a(n-7) -a(n-10)
%F A264628 n=3: [order 15]
%F A264628 n=4: [order 18] for n>21
%e A264628 Some solutions for n=4 k=4
%e A264628 ..5.11..7..4..9....5..2..7..4.14....1..6..7..4..9....1..2..7..4.14
%e A264628 ..6..0..1..2..3....6..0..1..9..3...10..0.12..2..3....6..0.12..9..3
%e A264628 .20.12.13.14..8...15.12.13.23..8...20..5.22.14..8...11..5.13.23..8
%e A264628 .16.10.22.19.24...20.10.11.19.24...16.17.11.19.13...20.10.22.19.24
%e A264628 .21.15.23.17.18...21.22.16.17.18...21.15.23.24.18...21.15.16.17.18
%Y A264628 Column 2 is A000079(n-1).
%K A264628 nonn,tabl
%O A264628 1,5
%A A264628 _R. H. Hardin_, Nov 19 2015