A264142 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 1,1.

2, 8, 4, 18, 27, 8, 45, 144, 125, 16, 125, 720, 1440, 512, 32, 320, 3600, 15488, 14400, 2197, 64, 832, 18000, 168948, 297920, 144000, 9261, 128, 2197, 90000, 1903336, 7001316, 5953600, 1440000, 39304, 256, 5733, 450000, 20768650, 163887724

Offset

1,1

Comments

Table starts

...2.....8.......18.........45..........125.............320...............832

...4....27......144........720.........3600...........18000.............90000

...8...125.....1440......15488.......168948.........1903336..........20768650

..16...512....14400.....297920......7001316.......163887724........3798503424

..32..2197...144000....5953600....302693857.....15238898080......758116015189

..64..9261..1440000..117534144..12968882161...1376159333484...147813083354689

.128.39304.14400000.2330885440.557669432592.125699825697364.29086230347332416

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

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

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

k=3: a(n) = 10*a(n-1) for n>2

k=4: [order 8]

k=5: [order 32]

k=6: [order 95]

Empirical for row n:

n=1: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) -9*a(n-4) +3*a(n-5) -a(n-6) +3*a(n-7) -a(n-8)

n=2: a(n) = 5*a(n-1) for n>3

n=3: [order 67]

n=4: [order 95]

Example

Some solutions for n=3 k=4
..0..1..2..6..4....6..1..2..3..4....6..1..8..9..4....6..7..5..9..4
..5..3..7.11.12...11..0.10..8..9....2..0..7.11..3....2..0..1..8..3
.10.17..9.16..8....7..5.12.13.17...10..5.12.16.17...10.11.15.13.17
.15.13.14.18.19...15.16.14.18.19...15.13.14.18.19...12.16.14.18.19

Crossrefs

Column 1 is A000079.

Column 2 is A056570(n+2).

Row 1 is A264054.

Sequence in context: A110003 A035302 A104772 * A088156 A019193 A369178

Adjacent sequences: A264139 A264140 A264141 * A264143 A264144 A264145

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 04 2015

Status

approved