A264207 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 0,2 or 1,0.

4, 18, 9, 81, 96, 25, 288, 1024, 605, 64, 1024, 7328, 14641, 3600, 169, 3872, 52441, 223245, 202500, 21853, 441, 14641, 422505, 3404025, 6444000, 2825761, 131712, 1156, 54450, 3404025, 59040000, 205062400, 189087285, 39337984, 795906, 3025

Offset

1,1

Comments

Table starts

.....4........18...........81...........288...........1024............3872

.....9........96.........1024..........7328..........52441..........422505

....25.......605........14641........223245........3404025........59040000

....64......3600.......202500.......6444000......205062400......7664479280

...169.....21853......2825761.....189087285....12652875225...1017895774965

...441....131712.....39337984....5520382336...774686906569.134248485475735

..1156....795906....547981281..161423594928.47551947307264

..3025...4804910...7632119044.4717876917930

..7921..29017649.106302733681

.20736.175219200

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +18*a(n-2) +5*a(n-3) -18*a(n-4) +3*a(n-5) +a(n-6)

k=3: a(n) = 11*a(n-1) +44*a(n-2) -44*a(n-3) -11*a(n-4) +a(n-5)

k=4: [order 30]

k=5: [order 51]

Empirical for row n:

n=1: a(n) = 4*a(n-1) -4*a(n-2) +12*a(n-3) -12*a(n-5) +4*a(n-6) -4*a(n-7) +a(n-8)

n=2: [order 92]

Example

Some solutions for n=3 k=4
..0..1..4..3..2....0..1..4..8..2....0..6..7..1..2....0..1..4..3..2
..5..8.12.13..7...10..6..5..3..7....5..8..9..3..4....5..8..7..6..9
.15..6.14.11..9...15.13.12.11..9...10.16.14.11.12...15.16.14.11.12
.10.18.19.16.17...17.18.19.16.14...15.18.17.13.19...10.18.17.13.19

Crossrefs

Column 1 is A007598(n+2).

Row 1 is A264004.

Sequence in context: A342153 A341800 A236563 * A264003 A077109 A070923

Adjacent sequences: A264204 A264205 A264206 * A264208 A264209 A264210

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 08 2015

Status

approved