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%I #6 Nov 10 2015 10:41:22
%S 1,2,1,4,4,1,8,16,8,1,16,48,64,16,1,32,144,288,256,32,1,64,432,1296,
%T 1728,1024,64,1,128,1296,6480,11664,10368,4096,128,1,256,3888,32400,
%U 97200,104976,62208,16384,256,1,512,11664,162000,810000,1458000,944784,373248
%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 index change +-(.,.) 0,0 or 1,2.
%C Table starts
%C .1....2.......4........8.........16............32..............64
%C .1....4......16.......48........144...........432............1296
%C .1....8......64......288.......1296..........6480...........32400
%C .1...16.....256.....1728......11664.........97200..........810000
%C .1...32....1024....10368.....104976.......1458000........20250000
%C .1...64....4096....62208.....944784......21870000.......506250000
%C .1..128...16384...373248....8503056.....328050000.....12656250000
%C .1..256...65536..2239488...76527504....4920750000....316406250000
%C .1..512..262144.13436928..688747536...73811250000...7910156250000
%C .1.1024.1048576.80621568.6198727824.1107168750000.197753906250000
%H R. H. Hardin, <a href="/A263989/b263989.txt">Table of n, a(n) for n = 1..479</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1)
%F k=3: a(n) = 4*a(n-1)
%F k=4: a(n) = 6*a(n-1)
%F k=5: a(n) = 9*a(n-1)
%F k=6: a(n) = 15*a(n-1) for n>2
%F k=7: a(n) = 25*a(n-1) for n>2
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: a(n) = 3*a(n-1) for n>3
%F n=3: a(n) = 5*a(n-1) for n>5
%F n=4: a(n) = 8*a(n-1) for n>7
%F n=5: a(n) = 13*a(n-1) for n>9
%F n=6: a(n) = 21*a(n-1) for n>11
%F n=7: a(n) = 34*a(n-1) for n>13
%e Some solutions for n=4 k=4
%e ..7..8..9..3..4....0..8..2..3..4....0..1..2..3..4....0..1..9..3..4
%e ..5..6..0..1..2...12.13.14..1..9...12..6..7..8..9....5..6..7..8..2
%e .17.18.12.13.14...10.11..5..6..7...10.18..5.13.14...10.18.19.13.14
%e .15.16.10.11.19...22.16.17.18.19...22.23.24.11.19...15.16.17.11.12
%e .20.21.22.23.24...20.21.15.23.24...20.21.15.16.17...20.21.22.23.24
%Y Column 2 is A000079.
%Y Column 3 is A000302.
%Y Row 1 is A000079(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Oct 31 2015
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