A264131 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 1,2.

1, 5, 1, 25, 13, 1, 80, 169, 34, 1, 256, 1040, 1156, 89, 1, 976, 6400, 13600, 7921, 233, 1, 3721, 53280, 160000, 178000, 54289, 610, 1, 13725, 443556, 2920000, 4000000, 2330000, 372100, 1597, 1, 50625, 3383280, 53290000, 160564000, 100000000

Offset

1,2

Comments

Table starts

.1.....5........25.........80.........256..........976.........3721

.1....13.......169.......1040........6400........53280.......443556

.1....34......1156......13600......160000......2920000.....53290000

.1....89......7921.....178000.....4000000....160564000...6445199524

.1...233.....54289....2330000...100000000...8830490000.779775536401

.1...610....372100...30500000..2500000000.485643650000

.1..1597...2550409..399250000.62500000000

.1..4181..17480761.5226250000

.1.10946.119814916

.1.28657

Links

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

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 15*a(n-1) -25*a(n-2)

k=5: a(n) = 25*a(n-1)

k=6: a(n) = 60*a(n-1) -300*a(n-2) +1500*a(n-3) -7500*a(n-4) +3125*a(n-5)

Empirical for row n:

n=1: a(n) = 4*a(n-1) -a(n-2) +15*a(n-4) -60*a(n-5) +15*a(n-6) -15*a(n-8) +60*a(n-9) -15*a(n-10) +a(n-12) -4*a(n-13) +a(n-14)

Example

Some solutions for n=4 k=4
..0..1..9..3..4....0..1..4..3..2....0..1..2..3..4....0..1..4..3..2
..7..8..5..6..2....5..8.14..6..9....5..8..7..6..9....7..8..5..6..9
.10.11.14.13.12...12.18.10.13..7...17.18.19.13.14...10.13.19.11.14
.15.16.24.18.19...15.16.19.11.17...15.23.10.11.12...22.18.15.16.12
.22.21.20.23.17...20.21.24.23.22...20.21.22.16.24...20.23.24.21.17

Crossrefs

Column 2 is A001519(n+2).

Column 3 is A081068(n+1).

Sequence in context: A218016 A193685 A174358 * A075500 A096645 A376582

Adjacent sequences: A264128 A264129 A264130 * A264132 A264133 A264134

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2015

Status

approved