A263816 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 0,1 0,2 or 1,0.

9, 82, 32, 572, 948, 121, 3682, 18776, 11305, 450, 25001, 333429, 643905, 134028, 1681, 170946, 6425985, 31916832, 21876416, 1590733, 6272, 1157993, 124854432, 1746531193, 3019386508, 744805993, 18875976, 23409, 7844192, 2392853088

Offset

1,1

Comments

Table starts

......9.........82..........572...........3682...........25001.........170946

.....32........948........18776.........333429.........6425985......124854432

....121......11305.......643905.......31916832......1746531193....96761217077

....450.....134028.....21876416.....3019386508....469723808009.74221751084228

...1681....1590733....744805993...286407546797.126619013196417

...6272...18875976..25345430544.27150876030959

..23409..223995034.862592912860

..87362.2658056430

.326041

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 10*a(n-1) +23*a(n-2) -10*a(n-3) -a(n-4)

k=3: [order 15]

k=4: [order 82]

Empirical for row n:

n=1: [linear recurrence of order 26]

Example

Some solutions for n=2 k=4
..0..1..3..2..4....0..3..2..8..4....0..6..2..8..4....0..3..2..8..4
..5..6..7..8..9....6..1.12..9..7....7..1..9..3.14....5..1..9..6..7
.12.10.11.14.13....5.10.13.11.14....5.11.10.13.12...12.10.11.14.13

Crossrefs

Column 1 is A006253(n+1).

Sequence in context: A061211 A115988 A067506 * A345143 A275917 A293803

Adjacent sequences: A263813 A263814 A263815 * A263817 A263818 A263819

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 27 2015

Status

approved