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 A264207 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 0,2 or 1,0. 9

%I

%S 4,18,9,81,96,25,288,1024,605,64,1024,7328,14641,3600,169,3872,52441,

%T 223245,202500,21853,441,14641,422505,3404025,6444000,2825761,131712,

%U 1156,54450,3404025,59040000,205062400,189087285,39337984,795906,3025

%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 0,2 or 1,0.

%C Table starts

%C .....4........18...........81...........288...........1024............3872

%C .....9........96.........1024..........7328..........52441..........422505

%C ....25.......605........14641........223245........3404025........59040000

%C ....64......3600.......202500.......6444000......205062400......7664479280

%C ...169.....21853......2825761.....189087285....12652875225...1017895774965

%C ...441....131712.....39337984....5520382336...774686906569.134248485475735

%C ..1156....795906....547981281..161423594928.47551947307264

%C ..3025...4804910...7632119044.4717876917930

%C ..7921..29017649.106302733681

%C .20736.175219200

%H R. H. Hardin, <a href="/A264207/b264207.txt">Table of n, a(n) for n = 1..71</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)

%F k=2: a(n) = 3*a(n-1) +18*a(n-2) +5*a(n-3) -18*a(n-4) +3*a(n-5) +a(n-6)

%F k=3: a(n) = 11*a(n-1) +44*a(n-2) -44*a(n-3) -11*a(n-4) +a(n-5)

%F k=4: [order 30]

%F k=5: [order 51]

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -4*a(n-2) +12*a(n-3) -12*a(n-5) +4*a(n-6) -4*a(n-7) +a(n-8)

%F n=2: [order 92]

%e Some solutions for n=3 k=4

%e ..0..1..4..3..2....0..1..4..8..2....0..6..7..1..2....0..1..4..3..2

%e ..5..8.12.13..7...10..6..5..3..7....5..8..9..3..4....5..8..7..6..9

%e .15..6.14.11..9...15.13.12.11..9...10.16.14.11.12...15.16.14.11.12

%e .10.18.19.16.17...17.18.19.16.14...15.18.17.13.19...10.18.17.13.19

%Y Column 1 is A007598(n+2).

%Y Row 1 is A264004.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 08 2015

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Last modified December 4 12:27 EST 2021. Contains 349495 sequences. (Running on oeis4.)