A264059 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 2,-2.

1, 2, 1, 4, 8, 1, 8, 64, 18, 1, 16, 216, 324, 45, 1, 32, 729, 2592, 2025, 125, 1, 64, 3375, 20736, 32400, 15625, 320, 1, 128, 15625, 207360, 518400, 450000, 102400, 832, 1, 256, 64000, 2073600, 11151360, 12960000, 5760000, 692224, 2197, 1, 512, 262144

Offset

1,2

Comments

Table starts

.1.....2.........4............8............16..............32..............64

.1.....8........64..........216...........729............3375...........15625

.1....18.......324.........2592.........20736..........207360.........2073600

.1....45......2025........32400........518400........11151360.......239878144

.1...125.....15625.......450000......12960000.......608212800.....28543426704

.1...320....102400......5760000.....324000000.....34260048000...3622687928896

.1...832....692224.....74880000....8100000000...1869178500000.431336822822500

.1..2197...4826809....988650000..202500000000.102920833800000

.1..5733..32867289..12899250000.5062500000000

.1.14994.224820036.168682500000

Links

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

Formula

Empirical for column k:

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

k=2: 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)

k=3: [order 17]

k=4: [order 8] for n>10

k=5: a(n) = 25*a(n-1) for n>3

Empirical for row n:

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

n=2: [order 12]

n=3: a(n) = 10*a(n-1) for n>5

n=4: [order 32]

Example

Some solutions for n=4 k=4
..0..1..9.11..4....0..1..9.11..4....0..1.10..3..4....0..8..9..3..4
..5..6..7.16..2....5..6..7..8..2....5..6.14..8..9....5.13..7..1..2
.17..3.19.21.14...10..3.20.13.22....2.18.12.21..7...10.11.20..6.22
.22..8.10.18.12...15.23.24.18.19...15.16.24.11.19...15.16.24.18.19
.20.13.15.23.24...12.21.14.16.17...20.13.22.23.17...12.21.14.23.17

Crossrefs

Row 1 is A000079(n-1).

Sequence in context: A220916 A221632 A071951 * A275364 A160323 A340469

Adjacent sequences: A264056 A264057 A264058 * A264060 A264061 A264062

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 02 2015

Status

approved