A264110 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 1,1.

2, 9, 4, 45, 40, 8, 144, 441, 169, 16, 512, 2745, 4410, 714, 32, 1936, 21025, 54756, 44100, 3025, 64, 7381, 167464, 911754, 1086300, 441000, 12816, 128, 27225, 1336336, 15437041, 39087504, 21511044, 4410000, 54289, 256, 101250, 10277652, 267205956

Offset

1,1

Comments

Table starts

...2......9.........45..........144...........512...........1936...........7381

...4.....40........441.........2745.........21025.........167464........1336336

...8....169.......4410........54756........911754.......15437041......267205956

..16....714......44100......1086300......39087504.....1399892079....52292712976

..32...3025.....441000.....21511044....1680100825...127528266321.10275868913985

..64..12816....4410000....426058380...72203451849.11613782698504

.128..54289...44100000...8439361956.3103083479700

.256.229970..441000000.167165327340

.512.974169.4410000000

Links

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

Formula

Empirical for column k:

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

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

k=3: a(n) = 10*a(n-1) for n>2

k=4: a(n) = 19*a(n-1) +304*a(n-3) +256*a(n-4)

k=5: [order 14]

Empirical for row n:

n=1: [linear recurrence of order 14]

Example

Some solutions for n=3 k=4
..0..3..2..1..4....6..3..4..1..2....6..7..8..1..4....6..3..0..9..4
..5.12..9.14..7...11..0..9.14..7....5..0..9..2..3....5..8..1..2..7
.10.11..6.13..8...10..5.12.13..8...16.11.10.13.14...16.13.18.11.14
.15.18.19.16.17...15.16.17.18.19...15.18.17.12.19...17.10.15.12.19

Crossrefs

Column 1 is A000079.

Sequence in context: A353242 A249596 A038215 * A119019 A268204 A268249

Adjacent sequences: A264107 A264108 A264109 * A264111 A264112 A264113

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2015

Status

approved