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

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Last modified November 26 17:30 EST 2022. Contains 358362 sequences. (Running on oeis4.)