A263602 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 filled by rows with each element moved a city block distance of 0 or 2, and rows and columns in increasing lexicographic order.

2, 7, 8, 15, 144, 24, 27, 1687, 1962, 60, 55, 13455, 69792, 24091, 160, 109, 105222, 1880912, 2736666, 317857, 448, 199, 747253, 51961032, 248766606, 123176874, 4177099, 1232, 347, 4989566, 1372902790, 25103852988, 40226420700, 5641347668

Offset

1,1

Comments

Table starts

....2.........7...........15............27.............55...........109

....8.......144.........1687.........13455.........105222........747253

...24......1962........69792.......1880912.......51961032....1372902790

...60.....24091......2736666.....248766606....25103852988.2343241421547

..160....317857....123176874...40226420700.14573046651208

..448...4177099...5641347668.6430889476830

.1232..54493144.249947653938

.3344.712019936

.9120

Links

R. H. Hardin, Table of n, a(n) for n = 1..49

Formula

Empirical for column k:

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

k=2: [order 53]

Empirical for row n:

n=1: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -a(n-4) -a(n-5) +a(n-6) for n>8

n=2: [order 73] for n>77

Example

Some solutions for n=3 k=4
..0..1..2..3..4....0..1..2..7.14....0..1..2..3.14....0..1..2..3..4
..5..6.11.18..9....5.12.13.18..3....5.12.11..6..9....5.12.17..6..9
.10..7.16.19..8...10.17..6.19..4...10..7.16.19..4...10.13.18..7..8
.15.12.13.14.17...15.16.11..8..9...15.18.17..8.13...15.16.11.14.19

Crossrefs

Sequence in context: A023178 A334227 A080572 * A162664 A341706 A032689

Adjacent sequences: A263599 A263600 A263601 * A263603 A263604 A263605

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 22 2015

Status

approved