A264878 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 -2,0 or 1,1.

1, 0, 1, 1, 0, 1, 0, 1, 0, 2, 1, 1, 5, 0, 3, 0, 7, 4, 20, 0, 4, 1, 20, 65, 12, 56, 0, 5, 0, 49, 228, 572, 36, 137, 0, 6, 1, 175, 1101, 2348, 3613, 108, 295, 0, 8, 0, 323, 4832, 22152, 22400, 19372, 324, 709, 0, 11, 1, 1085, 18501, 129230, 356692, 207424, 103585, 972, 1983, 0

Offset

1,10

Comments

Table starts

..1.0....1....0........1..........0............1..............0

..1.0....1....1........7.........20...........49............175

..1.0....5....4.......65........228.........1101...........4832

..2.0...20...12......572.......2348........22152.........129230

..3.0...56...36.....3613......22400.......356692........3303808

..4.0..137..108....19372.....207424......4747695.......78535556

..5.0..295..324...103585....1946752.....68488297.....1924357508

..6.0..709..972...629654...18265856...1050281271....47123513432

..8.0.1983.2916..3930725..171168256..16268725036..1152731721920

.11.0.5280.8748.23940621.1602206720.247512489984.28078658475952

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-5)

k=2: a(n) = a(n-1)

k=3: [order 45]

k=4: a(n) = 3*a(n-1) for n>3

Empirical for row n:

n=1: a(n) = a(n-2)

n=2: [order 20]

n=3: [order 46]

Example

Some solutions for n=4 k=4
..1..2..3..4.14...10..2.12..4.14....1..2.12..4.14...10..2..3..4.14
.15..0..8..9.19....6..0..1..9..3...15..0..8..9..3....6..0..1..9.19
.20..5..6..7.24...20..5.22..7..8...20..5..6..7.24...20..5.22..7..8
.16.10.11.12.13...16.17.11.19.13...16.10.11.19.13...16.17.11.12.13
.21.22.23.17.18...21.15.23.24.18...21.22.23.17.18...21.15.23.24.18

Crossrefs

Column 1 is A003520(n+1).

Column 4 is A003946(n-2).

Sequence in context: A257859 A231622 A165623 * A338035 A110243 A169950

Adjacent sequences: A264875 A264876 A264877 * A264879 A264880 A264881

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 27 2015

Status

approved