A263973 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 (+-,+-) 0,2 1,1 or 1,0.

4, 20, 0, 108, 72, 16, 465, 1817, 1441, 0, 2265, 10720, 86633, 13856, 64, 10920, 89472, 2604481, 2940624, 189993, 0, 52752, 1791696, 102742049, 226810352, 118376593, 2215960, 256, 253176, 27783305, 4952396901, 24130893568, 31702909989

Offset

1,1

Comments

Table starts

....4........20..........108...........465...........2265.........10920

....0........72.........1817.........10720..........89472.......1791696

...16......1441........86633.......2604481......102742049....4952396901

....0.....13856......2940624.....226810352....24130893568.4071813326144

...64....189993....118376593...31702909989.11743850653769

....0...2215960...4465927225.3594130469760

..256..28027420.173624682220

....0.340646784

.1024

Links

R. H. Hardin, Table of n, a(n) for n = 1..49

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-2)

k=2: [order 10]

k=3: [order 27]

k=4: [order 53]

Empirical for row n:

n=1: [linear recurrence of order 22]

Example

Some solutions for n=3 k=4
..2..3..6..9..8....2..3..6..1..9....2..5..4..1..8....2..5..4..9..8
..7..0..1..4.14....7..0..5.12..4....7..0..3.14.13....7..0..1.13..3
..5.15.17.18.19...16.15..8.17.18....6.16.18.19..9...12..6.17.19.18
.10.12.11.16.13...10.11.19.13.14...11.10.15.12.17...11.10.15.16.14

Crossrefs

Column 1 is A199572(n+1).

Row 1 is A263965.

Sequence in context: A291947 A023994 A002813 * A364519 A104159 A039921

Adjacent sequences: A263970 A263971 A263972 * A263974 A263975 A263976

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 30 2015

Status

approved