A264257 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,1 0,-1 0,2 1,0 or -1,0.

4, 10, 9, 29, 33, 25, 89, 157, 180, 64, 260, 1124, 1920, 760, 169, 772, 5468, 23805, 14893, 3653, 441, 2281, 32361, 254393, 397462, 147797, 16401, 1156, 6741, 181644, 2896729, 7877184, 7467925, 1273553, 76330, 3025, 19940, 1005279, 32417000

Offset

1,1

Comments

Table starts

.....4......10.........29.............89.............260..............772

.....9......33........157...........1124............5468............32361

....25.....180.......1920..........23805..........254393..........2896729

....64.....760......14893.........397462.........7877184........180566464

...169....3653.....147797........7467925.......301623757......13509166173

...441...16401....1273553......132080760.....10265640512.....917543249651

..1156...76330...11868873.....2411543681....372797128908...65622177560404

..3025..348480..105792288....43298007242..13053476555570.4563171069771635

..7921.1607429..966768105...784323747917.466441716294953

.20736.7373520.8711282401.14141096261412

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +16*a(n-2) +9*a(n-3) -29*a(n-4) -9*a(n-5) +16*a(n-6) -a(n-7) -a(n-8)

k=3: [order 33]

Empirical for row n:

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

n=2: [order 47]

Example

Some solutions for n=3 k=4
..1..0..7..8..3....5..6..1..4..2....5..2..3..4..9....5..2..0..1..3
.10.11..2..6..4....0..7..8..3.14....0..1..8.13..7....6.11.12..7..4
..5.12.13.14..9...11.16.13.12..9...15..6.17.18.19...15.16.13..8..9
.16.17.15.19.18...10.15.18.19.17...10.11.12.16.14...10.17.18.19.14

Crossrefs

Column 1 is A007598(n+2).

Row 1 is A264158.

Sequence in context: A053248 A081547 A264272 * A111072 A189895 A310333

Adjacent sequences: A264254 A264255 A264256 * A264258 A264259 A264260

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 09 2015

Status

approved