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A264003 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 1,2 or 1,0. 9

%I

%S 4,18,9,81,99,25,288,1089,925,64,1024,8679,34225,7304,169,3872,69169,

%T 791245,833569,62101,441,14641,568343,18292729,50616720,22819729,

%U 516117,1156,54450,4669921,457981160,3073593600,3817152613,604028929,4331090

%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 1,2 or 1,0.

%C Table starts

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

%C ....9.......99........1089.........8679........69169.......568343

%C ...25......925.......34225.......791245.....18292729....457981160

%C ...64.....7304......833569.....50616720...3073593600.209279846160

%C ..169....62101....22819729...3817152613.638511266761

%C ..441...516117...604028929.271516496545

%C .1156..4331090.16226938225

%C .3025.36234055

%C .7921

%H R. H. Hardin, <a href="/A264003/b264003.txt">Table of n, a(n) for n = 1..49</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) = 5*a(n-1) +37*a(n-2) -44*a(n-3) -256*a(n-4) +64*a(n-5) +256*a(n-6)

%F k=3: a(n) = 29*a(n-1) +36*a(n-2) -2832*a(n-3) +6656*a(n-4) +24576*a(n-5) -65536*a(n-6)

%F k=4: [order 30]

%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 16]

%e Some solutions for n=3 k=4

%e ..0..8..2..3..9....0..6..7..8..4....0..1..2..3..7....0..1..2..6..7

%e ..5..1..4.13.12....5..3..2..1.12....5.13..4.11.14....5.13..4..3.12

%e .10.18..7..6.14...10.16.19.18..9...10..6.12..8..9...17.16..9..8.14

%e .15.16.17.11.19...15.13.17.11.14...15.16.17.18.19...15.11.10.18.19

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 31 2015

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Last modified October 26 17:38 EDT 2021. Contains 348268 sequences. (Running on oeis4.)