A264476 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 1,0 2,1 or -1,-1.

0, 1, 1, 0, 2, 0, 0, 4, 4, 1, 1, 8, 6, 8, 1, 0, 17, 16, 16, 16, 1, 0, 36, 57, 120, 49, 32, 2, 1, 76, 160, 456, 456, 124, 64, 2, 0, 160, 484, 2272, 3540, 2232, 384, 128, 3, 0, 337, 1449, 11044, 28489, 24773, 10116, 1041, 256, 4, 1, 710, 4250, 49200, 215607, 310748

Offset

1,5

Comments

Table starts

.0...1....0......0........1..........0............0..............1

.1...2....4......8.......17.........36...........76............160

.0...4....6.....16.......57........160..........484...........1449

.1...8...16....120......456.......2272........11044..........49200

.1..16...49....456.....3540......28489.......215607........1711113

.1..32..124...2232....24773.....310748......4039259.......50217832

.2..64..384..10116...174927....3842048.....74367790.....1462247321

.2.128.1041..45792..1262270...43644384...1358980008....44706530288

.3.256.2868.212112..8905776..505769648..25131223920..1299344783466

.4.512.8189.960336.63373156.5849013488.454913826610.38128043682868

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: [order 15]

k=4: a(n) = 18*a(n-2) +36*a(n-3) -45*a(n-4) -216*a(n-5) -243*a(n-6) for n>7

k=5: [order 84] for n>86

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

Empirical for row n:

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

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

n=3: [order 15]

n=4: [order 10] for n>11

n=5: [order 84]

Example

Some solutions for n=4 k=4
..6..0..1..9..3....6..0..1..2..3....6..7..8..9..3....6..7..8..2..3
.11..5..2..7..4...11.12.13.14..4....0..1..2.14..4....0..1.13.14..4
.16.10.18..8.13....5.10..7.19..9...16.10.11.19.13...16.17.11.12..9
.21.22.23.24.14...21.22.16.24..8...21..5.12.24.18...10..5.23.24.18
.15.20.17.12.19...15.20.17.18.23...15.20.17.22.23...15.20.21.22.19

Crossrefs

Column 1 is A000931(n+1).

Column 2 is A000079(n-1).

Row 2 is A008999(n-1).

Sequence in context: A137830 A137828 A264655 * A342276 A137505 A107498

Adjacent sequences: A264473 A264474 A264475 * A264477 A264478 A264479

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 14 2015

Status

approved