A264172 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 -2,-1 or -1,-2.

1, 4, 4, 8, 25, 8, 16, 98, 98, 16, 33, 418, 733, 418, 33, 69, 1862, 6017, 6017, 1862, 69, 145, 8007, 50237, 96296, 50237, 8007, 145, 300, 34539, 408698, 1531900, 1531900, 408698, 34539, 300, 624, 149808, 3328825, 23916656, 47277776, 23916656, 3328825

Offset

1,2

Comments

Table starts

....1.......4..........8............16...............33................69

....4......25.........98...........418.............1862..............8007

....8......98........733..........6017............50237............408698

...16.....418.......6017.........96296..........1531900..........23916656

...33....1862......50237.......1531900.........47277776........1432853288

...69....8007.....408698......23916656.......1432853288.......83609564805

..145...34539....3328825.....375202191......43416669841.....4868342507373

..300..149808...27209977....5888212022....1312690666360...283367589816531

..624..648436..222177128...92168640612...39639424508160.16469467179397573

.1300.2805250.1813435208.1442827111989.1196969465424056

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +7*a(n-2) +23*a(n-3) +35*a(n-4) +18*a(n-5) for n>7

k=3: [order 56]

Example

Some solutions for n=4 k=4
..7..1..2..3..4....0..8..1..2..3....0..1..2.14..3....0..1.13..2..3
..0.13..6.19..9....5.13.14..7..4...12..5..6..7..4....5..6..7..8..4
..5.10.11..8.14...10..6.12.24..9...10.22.11..8..9...17.10.19.12..9
.22.16.12.17.18...15.11.17.18.19...15.23.17.13.19...15.11.16.18.14
.15.20.21.23.24...20.16.21.22.23...20.16.21.18.24...20.21.22.23.24

Crossrefs

Sequence in context: A019171 A038551 A004049 * A019122 A019202 A137717

Adjacent sequences: A264169 A264170 A264171 * A264173 A264174 A264175

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 06 2015

Status

approved