A264217 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,0 0,1 1,0 -1,0 or 0,-2.

4, 17, 9, 56, 96, 25, 172, 623, 596, 64, 561, 3736, 7949, 3610, 169, 1826, 24908, 97332, 97520, 21997, 441, 5880, 163505, 1333336, 2407816, 1210573, 133836, 1156, 18993, 1056337, 17998869, 68008846, 60472721, 14973263, 814609, 3025, 61424, 6877345

Offset

1,1

Comments

Table starts

....4.......17..........56............172...............561...............1826

....9.......96.........623...........3736.............24908.............163505

...25......596........7949..........97332...........1333336...........17998869

...64.....3610.......97520........2407816..........68008846.........1883268032

..169....21997.....1210573.......60472721........3516298221.......200034582505

..441...133836....14973263.....1511983080......181148689096.....21168809029549

.1156...814609...185410184....37854981564.....9342273315041...2243001383143442

.3025..4957760..2295059475...947369885896...481661295203904.237592988053853489

.7921.30173957.28412159649.23712132417625.24835326206594357

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

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

k=2: [order 8]

k=3: [order 23]

Empirical for row n:

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

n=2: [order 46]

Example

Some solutions for n=3 k=4
..0..3..2..8..4....2..0..1..8..3....0..3..4..2..9....0..3..1..2..4
..5..1..6..7..9....5..6..9..7..4...10..1..6..7.14...10..5..7..8..9
.10.11.12.18.14...15.11.12.18.14....5.16.17..8.19...12..6.11.13.19
.17.15.16.13.19...10.16.17.13.19...15.11.12.13.18...15.16.17.18.14

Crossrefs

Column 1 is A007598(n+2).

Sequence in context: A368392 A116573 A195881 * A341442 A063625 A373414

Adjacent sequences: A264214 A264215 A264216 * A264218 A264219 A264220

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 08 2015

Status

approved