A263586 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 1 or 2, and rows and columns in increasing lexicographic order.

1, 6, 4, 12, 134, 18, 31, 1992, 3035, 70, 89, 27650, 145151, 69084, 292, 230, 343431, 8296414, 14088801, 1643235, 1212, 536, 3777963, 479355276, 3822509358, 1544467524, 38562523, 5028, 1171, 38762619, 24453863816, 1035523589834

Offset

1,2

Comments

Table starts

.....1.........6...........12............31............89.............230

.....4.......134.........1992.........27650........343431.........3777963

....18......3035.......145151.......8296414.....479355276.....24453863816

....70.....69084.....14088801....3822509358.1035523589834.244734723702847

...292...1643235...1544467524.1954083613268

..1212..38562523.162168224979

..5028.903637375

.20832

Links

R. H. Hardin, Table of n, a(n) for n = 1..40

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) +2*a(n-3) +4*a(n-4) -8*a(n-5)

k=2: [order 84]

Empirical for row n:

n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) -2*a(n-5) +3*a(n-6) -a(n-8) for n>9

Example

Some solutions for n=3 k=4
..1..3..4..7..9....1..5..7..9.14....1..3..4..7..9....1..5..7..8..9
..6..0..5..2..8....6..0..2.12..4....6..0..5..2..8....6..0.12.13..3
.11.15.10.19.12...11.15..8..3.13...11.15.10.19.18...11.15..2.14..4
.16.17.18.13.14...17.10.16.19.18...17.12.16.13.14...17.10.19.16.18

Crossrefs

Sequence in context: A040032 A239394 A006582 * A180497 A213038 A337512

Adjacent sequences: A263583 A263584 A263585 * A263587 A263588 A263589

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 22 2015

Status

approved