A264422 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 0,1 2,2 1,0 -1,2 -2,-1 or -1,-1.

0, 2, 1, 0, 3, 1, 0, 12, 20, 1, 4, 37, 96, 85, 1, 0, 119, 499, 529, 351, 3, 0, 385, 2681, 7311, 4843, 1462, 3, 8, 1252, 15088, 101862, 137584, 44264, 6021, 4, 0, 4061, 86469, 1103666, 4023076, 2486429, 352713, 25188, 6, 0, 13166, 479787, 13805196, 95946259

Offset

1,2

Comments

Table starts

.0......2.........0...........0............4............0............0

.1......3........12..........37..........119..........385.........1252

.1.....20........96.........499.........2681........15088........86469

.1.....85.......529........7311.......101862......1103666.....13805196

.1....351......4843......137584......4023076.....95946259...2486418295

.3...1462.....44264.....2486429....147984724...7577203142.396849643846

.3...6021....352713....40217261...5498758183.577598946184

.4..25188...2840274...681146169.201733617932

.6.104870..23795758.11846231201

.9.437164.197390196

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

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

k=2: [order 56]

k=3: [order 70]

Empirical for row n:

n=1: a(n) = 2*a(n-3)

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

n=3: [order 33]

n=4: [order 16] for n>18

Example

Some solutions for n=4 k=4
..6..7..8..2..3....6..7..8..2..3....6..0..8..9..3....6.12.13.14..3
..0..1.13.19..4...11..1.13.19..4...16..1..2..7..4....0..1..2.19..4
..5.17.18.12..9....5.17..0.12..9....5.17.11.19.13...16.10..7..8..9
.21.22.20.24.14...10.22.16.24.14...10.22.23.24.14...21.11..5.24.22
.15.16.10.11.23...15.20.21.18.23...15.20.21.18.12...15.20.17.18.23

Crossrefs

Column 1 is A080013(n+1).

Sequence in context: A029293 A218254 A285037 * A376498 A176808 A327029

Adjacent sequences: A264419 A264420 A264421 * A264423 A264424 A264425

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 12 2015

Status

approved