A264190 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,-1 or 2,2.

2, 4, 4, 8, 24, 8, 16, 81, 81, 16, 32, 375, 720, 375, 32, 64, 1600, 7056, 7056, 1600, 64, 128, 6656, 70560, 147968, 70560, 6656, 128, 256, 28561, 705600, 2944656, 2944656, 705600, 28561, 256, 512, 120393, 7056000, 57950000, 130196484, 57950000, 7056000

Offset

1,1

Comments

Table starts

....2.......4..........8............16................32.................64

....4......24.........81...........375..............1600...............6656

....8......81........720..........7056.............70560.............705600

...16.....375.......7056........147968...........2944656...........57950000

...32....1600......70560.......2944656.........130196484.........5479256484

...64....6656.....705600......57950000........5479256484.......499844745900

..128...28561....7056000....1150295056......236489590800.....45243595984896

..256..120393...70560000...22732293168....10133933691456...4139503087656960

..512..509796..705600000..450192689296...435454125148224.376732468150329600

.1024.2161720.7056000000.8919674478000.18715402270845504

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: [order 14]

k=3: a(n) = 10*a(n-1) for n>4

k=4: [order 13]

k=5: [order 58]

Example

Some solutions for n=4 k=4
..0.13..2..3..8....0..1..6..3..4....0..1.14..3..4....0.13..6..3..8
..1.10..7..4..9...17..2.11..8..9...17..6.11.12..9...17.10.11..4..9
..6.11.16.17.14...10..7.12.13.14...10.23..8.13..2...22..7.16..1..2
.15.12..5.22.23...15.20..5.22.19...15.16..5.18..7...15.12..5.14.23
.20.21.18.19.24...16.21.18.23.24...20.21.22.19.24...20.21.18.19.24

Crossrefs

Column 1 is A000079.

Sequence in context: A295293 A080007 A239649 * A006967 A296229 A322175

Adjacent sequences: A264187 A264188 A264189 * A264191 A264192 A264193

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 06 2015

Status

approved