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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)