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A264422 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 0,1 2,2 1,0 -1,2 -2,-1 or -1,-1.

%I A264422 #4 Nov 12 2015 23:01:42
%S A264422 0,2,1,0,3,1,0,12,20,1,4,37,96,85,1,0,119,499,529,351,3,0,385,2681,
%T A264422 7311,4843,1462,3,8,1252,15088,101862,137584,44264,6021,4,0,4061,
%U A264422 86469,1103666,4023076,2486429,352713,25188,6,0,13166,479787,13805196,95946259
%N A264422 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 0,1 2,2 1,0 -1,2 -2,-1 or -1,-1.
%C A264422 Table starts
%C A264422 .0......2.........0...........0............4............0............0
%C A264422 .1......3........12..........37..........119..........385.........1252
%C A264422 .1.....20........96.........499.........2681........15088........86469
%C A264422 .1.....85.......529........7311.......101862......1103666.....13805196
%C A264422 .1....351......4843......137584......4023076.....95946259...2486418295
%C A264422 .3...1462.....44264.....2486429....147984724...7577203142.396849643846
%C A264422 .3...6021....352713....40217261...5498758183.577598946184
%C A264422 .4..25188...2840274...681146169.201733617932
%C A264422 .6.104870..23795758.11846231201
%C A264422 .9.437164.197390196
%H A264422 R. H. Hardin, <a href="/A264422/b264422.txt">Table of n, a(n) for n = 1..84</a>
%F A264422 Empirical for column k:
%F A264422 k=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)
%F A264422 k=2: [order 56]
%F A264422 k=3: [order 70]
%F A264422 Empirical for row n:
%F A264422 n=1: a(n) = 2*a(n-3)
%F A264422 n=2: a(n) = 3*a(n-1) +a(n-3) +5*a(n-4) +a(n-7)
%F A264422 n=3: [order 33]
%F A264422 n=4: [order 16] for n>18
%e A264422 Some solutions for n=4 k=4
%e A264422 ..6..7..8..2..3....6..7..8..2..3....6..0..8..9..3....6.12.13.14..3
%e A264422 ..0..1.13.19..4...11..1.13.19..4...16..1..2..7..4....0..1..2.19..4
%e A264422 ..5.17.18.12..9....5.17..0.12..9....5.17.11.19.13...16.10..7..8..9
%e A264422 .21.22.20.24.14...10.22.16.24.14...10.22.23.24.14...21.11..5.24.22
%e A264422 .15.16.10.11.23...15.20.21.18.23...15.20.21.18.12...15.20.17.18.23
%Y A264422 Column 1 is A080013(n+1).
%K A264422 nonn,tabl
%O A264422 1,2
%A A264422 _R. H. Hardin_, Nov 12 2015