A264583 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 1,0 0,-1 1,2 or -1,1.

0, 1, 1, 0, 2, 0, 1, 4, 4, 0, 1, 10, 4, 8, 1, 1, 16, 28, 6, 16, 0, 3, 56, 97, 104, 25, 32, 0, 1, 128, 333, 553, 505, 68, 64, 1, 3, 320, 1380, 2232, 3668, 2144, 112, 128, 0, 6, 784, 4497, 21312, 30718, 24370, 8185, 281, 256, 0, 5, 1792, 16712, 86812, 366292, 314166

Offset

1,5

Comments

Table starts

.0...1....0......1........1..........1...........3...........1...........3

.1...2....4.....10.......16.........56.........128.........320.........784

.0...4....4.....28.......97........333........1380........4497.......16712

.0...8....6....104......553.......2232.......21312.......86812......553861

.1..16...25....505.....3668......30718......366292.....2509523....26091488

.0..32...68...2144....24370.....314166.....5469993....64600334...955403058

.0..64..112...8185...145761....2561017....80571013..1370091018.31774873994

.1.128..281..33056...905291...24729380..1220343344.31418295732

.0.256..856.141037..5678975..248623843.18239876421

.0.512.1674.570758.35331350.2294091610

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

k=1: a(n) = a(n-3)

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

k=3: [order 15]

k=4: a(n) = 2*a(n-1) +36*a(n-3) +9*a(n-4) -243*a(n-6) for n>7

k=5: [order 84]

k=6: [order 36] for n>40

Empirical for row n:

n=1: a(n) = a(n-3) +a(n-4) +2*a(n-5) -a(n-9) -a(n-10)

n=2: a(n) = 2*a(n-1) +16*a(n-5) -16*a(n-6) +32*a(n-7) -64*a(n-10)

Example

Some solutions for n=4 k=4
..1..2..3..7..8....1..2..3..4..8....1..2..3..7..8....1..5..3..4..8
..0.10.11.12..4....0..7.11..9.13....0.10.11..9..4....6.10..0..9..2
..5.15.13..6..9....5..6.16.14.18....5.15.13..6.18...11.15..7.17.18
.16.20.18.19.14...10.20.12.19.23...16.20.12.19.14...16.20.12.13.14
.21.22.23.24.17...21.22.15.24.17...21.22.23.24.17...21.22.23.24.19

Crossrefs

Column 2 is A000079(n-1).

Sequence in context: A342321 A098689 A288515 * A158984 A158417 A139435

Adjacent sequences: A264580 A264581 A264582 * A264584 A264585 A264586

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 18 2015

Status

approved