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A264490 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,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

%I A264490 #6 Nov 14 2015 16:51:10
%S A264490 1,1,3,1,1,4,1,10,12,12,1,8,36,16,25,1,35,108,212,214,52,1,42,324,788,
%T A264490 2144,324,121,1,130,972,4772,21466,9714,2960,261,1,194,2916,23076,
%U A264490 217049,142352,92052,6442,576,1,501,8748,122628,2186741,2517024,2870927,581575
%N A264490 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,-1 1,0 2,1 0,-1 -2,-2 or -1,0.
%C A264490 Table starts
%C A264490 ....1......1........1..........1...........1...........1...........1
%C A264490 ....3......1.......10..........8..........35..........42.........130
%C A264490 ....4.....12.......36........108.........324.........972........2916
%C A264490 ...12.....16......212........788........4772.......23076......122628
%C A264490 ...25....214.....2144......21466......217049.....2186741....22085009
%C A264490 ...52....324.....9714.....142352.....2517024....42169152...714303376
%C A264490 ..121...2960....92052....2870927....89130069..2775259622.86190450233
%C A264490 ..261...6442...581575...30309632..1749889912.98973991195
%C A264490 ..576..42656..4510937..463508815.47485981944
%C A264490 .1280.113575.31398740.5517128232
%H A264490 R. H. Hardin, <a href="/A264490/b264490.txt">Table of n, a(n) for n = 1..98</a>
%F A264490 Empirical for column k:
%F A264490 k=1: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) +4*a(n-5) +a(n-6) -a(n-9)
%F A264490 k=2: [order 36]
%F A264490 Empirical for row n:
%F A264490 n=1: a(n) = a(n-1)
%F A264490 n=2: a(n) = 3*a(n-2) +2*a(n-3) +a(n-4) -a(n-5)
%F A264490 n=3: a(n) = 3*a(n-1)
%F A264490 n=4: a(n) = a(n-1) +16*a(n-2) +24*a(n-3) +16*a(n-4) +32*a(n-5) +32*a(n-6)
%F A264490 n=5: [order 39]
%F A264490 n=6: [order 10] for n>11
%e A264490 Some solutions for n=4 k=4
%e A264490 ..5..6..7..8..9....5..6..7..4..9....5..6..7..8..9....5..2..7..8..9
%e A264490 ..0.11..2.13.14...10.11.12.13.14...10.11..2.13..4....0.11.12..3..4
%e A264490 .22.16..1..4..3...22..0..1..2..3...22..0..1.14..3...22.16..1.18.19
%e A264490 .20.21.18.23.24...20.21..8.23.24...20.21.18.23.24...20.21..6.23.14
%e A264490 .15.10.17.12.19...15.16.17.18.19...15.16.17.12.19...15.10.17.24.13
%Y A264490 Row 3 is A003946.
%K A264490 nonn,tabl
%O A264490 1,3
%A A264490 _R. H. Hardin_, Nov 14 2015