A264379 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 2,-2 -1,0 -1,2 1,0 or 0,-1.

1, 2, 0, 4, 1, 1, 6, 6, 13, 0, 9, 9, 80, 25, 1, 15, 61, 385, 441, 128, 0, 25, 121, 2345, 3778, 3249, 347, 1, 40, 544, 14329, 60858, 63575, 22484, 1343, 0, 64, 1357, 88264, 711068, 1742881, 828400, 156293, 4172, 1, 104, 5100, 538417, 9407584, 45132986, 48714516

Offset

1,2

Comments

Table starts

.1.....2.......4..........6.............9..............15.................25

.0.....1.......6..........9............61.............121................544

.1....13......80........385..........2345...........14329..............88264

.0....25.....441.......3778.........60858..........711068............9407584

.1...128....3249......63575.......1742881........45132986.........1187897216

.0...347...22484.....828400......48714516......2546661201.......135926940964

.1..1343..156293...11888603....1363452981....149731056598.....16353452350876

.0..4172.1097881..163298870...38221084820...8620411258657...1906883090233889

.1.14711.7657324.2275569624.1068788896516.499872831041401.225710195773223581

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

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

k=2: [order 20]

k=3: [order 64]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-3) +a(n-4)

n=2: [order 10]

n=3: [order 70]

n=4: [order 81] for n>85

Example

Some solutions for n=4 k=4
..1..2..5..4..9....1..6..5..4..7....1..2..5..6..9....5..2..3..6..7
..0..7.10..3.14....0.11..2..3.14....0..7.10.11.14....0..1.10..9..4
.11..6.15.16.17...15.16.13..8..9...15..3..4..8.17...11.12.13.14.17
.20..8.18.21.22...10.17.20.21.24...16.21.20.13.24...20..8.22.21.24
.12.13.23.24.19...12.22.23.18.19...12.22.23.18.19...15.16.23.18.19

Crossrefs

Row 1 is A006498(n+1).

Sequence in context: A370412 A355917 A304789 * A090888 A154794 A177264

Adjacent sequences: A264376 A264377 A264378 * A264380 A264381 A264382

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 12 2015

Status

approved