A264313 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.

1, 6, 1, 20, 20, 1, 52, 139, 68, 1, 140, 735, 1032, 240, 1, 392, 4103, 11206, 7821, 832, 1, 1117, 24153, 130041, 167348, 58589, 2896, 1, 3155, 137703, 1605061, 3932500, 2495425, 440001, 10080, 1, 8845, 781453, 18898817, 101336088, 119041793

Offset

1,2

Comments

Table starts

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

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

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

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

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

.1...2896.....440001.....37246076....3604351803...402225464956.41578820903929

.1..10080....3303761....555887421..109088196333.25275285536728

.1..35072...24804389...8296387518.3301600532164

.1.122048..186235917.123820898705

.1.424704.1398284827

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

Formula

Empirical for column k:

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

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

k=3: [order 15]

k=4: [order 21]

k=5: [order 28]

Empirical for row n:

n=1: [linear recurrence of order 14]

n=2: [order 11]

Example

Some solutions for n=4 k=4
..0..1..2..3..4....0..1..2..3..4....7..0..1..3..4....7..1..9..3..4
.12.13..7..6..9...12.13.14..7..8...12..5..2..6..9....0.13..2..6..8
..5.11.19..8.14....5..6.10.11..9...17.10.11..8.14....5.10.12.11.14
.10.15.24.16.17...22.16.24.18.17...22.15.24.13.18...22.23.15.18.19
.20.21.22.18.23...15.20.21.23.19...20.16.21.23.19...20.16.17.21.24

Crossrefs

Sequence in context: A334504 A161151 A146383 * A096130 A120666 A050300

Adjacent sequences: A264310 A264311 A264312 * A264314 A264315 A264316

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 11 2015

Status

approved