A264313 - OEIS

%I #4 Nov 11 2015 09:58:37

%S 1,6,1,20,20,1,52,139,68,1,140,735,1032,240,1,392,4103,11206,7821,832,

%T 1,1117,24153,130041,167348,58589,2896,1,3155,137703,1605061,3932500,

%U 2495425,440001,10080,1,8845,781453,18898817,101336088,119041793

%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 directed index change 0,0 0,1 1,0 -1,-2 or 0,2.

%C Table starts

%C .1......6.........20...........52...........140............392...........1117

%C .1.....20........139..........735..........4103..........24153.........137703

%C .1.....68.......1032........11206........130041........1605061.......18898817

%C .1....240.......7821.......167348.......3932500......101336088.....2478206839

%C .1....832......58589......2495425.....119041793.....6395409906...322126444477

%C .1...2896.....440001.....37246076....3604351803...402225464956.41578820903929

%C .1..10080....3303761....555887421..109088196333.25275285536728

%C .1..35072...24804389...8296387518.3301600532164

%C .1.122048..186235917.123820898705

%C .1.424704.1398284827

%H R. H. Hardin, <a href="/A264313/b264313.txt">Table of n, a(n) for n = 1..83</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

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

%F k=3: [order 15]

%F k=4: [order 21]

%F k=5: [order 28]

%F Empirical for row n:

%F n=1: [linear recurrence of order 14]

%F n=2: [order 11]

%e Some solutions for n=4 k=4

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

%e .12.13..7..6..9...12.13.14..7..8...12..5..2..6..9....0.13..2..6..8

%e ..5.11.19..8.14....5..6.10.11..9...17.10.11..8.14....5.10.12.11.14

%e .10.15.24.16.17...22.16.24.18.17...22.15.24.13.18...22.23.15.18.19

%e .20.21.22.18.23...15.20.21.23.19...20.16.21.23.19...20.16.17.21.24

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 11 2015