A264003 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 1,2 or 1,0.

4, 18, 9, 81, 99, 25, 288, 1089, 925, 64, 1024, 8679, 34225, 7304, 169, 3872, 69169, 791245, 833569, 62101, 441, 14641, 568343, 18292729, 50616720, 22819729, 516117, 1156, 54450, 4669921, 457981160, 3073593600, 3817152613, 604028929, 4331090

Offset

1,1

Comments

Table starts

....4.......18..........81..........288.........1024.........3872

....9.......99........1089.........8679........69169.......568343

...25......925.......34225.......791245.....18292729....457981160

...64.....7304......833569.....50616720...3073593600.209279846160

..169....62101....22819729...3817152613.638511266761

..441...516117...604028929.271516496545

.1156..4331090.16226938225

.3025.36234055

.7921

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) +37*a(n-2) -44*a(n-3) -256*a(n-4) +64*a(n-5) +256*a(n-6)

k=3: a(n) = 29*a(n-1) +36*a(n-2) -2832*a(n-3) +6656*a(n-4) +24576*a(n-5) -65536*a(n-6)

k=4: [order 30]

Empirical for row n:

n=1: a(n) = 4*a(n-1) -4*a(n-2) +12*a(n-3) -12*a(n-5) +4*a(n-6) -4*a(n-7) +a(n-8)

n=2: [order 16]

Example

Some solutions for n=3 k=4
..0..8..2..3..9....0..6..7..8..4....0..1..2..3..7....0..1..2..6..7
..5..1..4.13.12....5..3..2..1.12....5.13..4.11.14....5.13..4..3.12
.10.18..7..6.14...10.16.19.18..9...10..6.12..8..9...17.16..9..8.14
.15.16.17.11.19...15.13.17.11.14...15.16.17.18.19...15.11.10.18.19

Crossrefs

Column 1 is A007598(n+2).

Sequence in context: A341800 A236563 A264207 * A077109 A070923 A064220

Adjacent sequences: A264000 A264001 A264002 * A264004 A264005 A264006

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 31 2015

Status

approved