A264163 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 0,1 0,-1 0,2 1,0 -1,0 or 2,0.

4, 10, 10, 29, 72, 29, 89, 412, 412, 89, 260, 2927, 5296, 2927, 260, 772, 19204, 82167, 82167, 19204, 772, 2281, 126688, 1149961, 2765728, 1149961, 126688, 2281, 6741, 845296, 16609233, 86079818, 86079818, 16609233, 845296, 6741, 19940, 5596616

Offset

1,1

Comments

Table starts

.....4........10...........29.............89..............260..............772

....10........72..........412...........2927............19204...........126688

....29.......412.........5296..........82167..........1149961.........16609233

....89......2927........82167........2765728.........86079818.......2726236497

...260.....19204......1149961.......86079818.......5865099776.....408612967960

...772....126688.....16609233.....2726236497.....408612967960...62592982984064

..2281....845296....239550224....86548482676...28536242142800.9610501585172009

..6741...5596616...3438669140..2736421213693.1983317242018219

.19940..37146638..49526113317.86706789763033

.58954.246557278.712398787569

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +2*a(n-2) +2*a(n-3) +4*a(n-5) -a(n-8)

k=2: [order 84]

Example

Some solutions for n=3 k=4
..1..0..3..4..2....1..0..3..4..9....5..2..3..1..9....5..2..0..4..3
..6..5..8..9..7...10..7..2..6.14....0..7..6.13..8....6..1..8.13.14
.11.10.17.12.19...15.16.11..8.13...15.16.17.14..4...11.16.17.12..9
.16.15.18.13.14....5.17.12.19.18...10.11.12.19.18...10.15..7.19.18

Crossrefs

Sequence in context: A201836 A201216 A184277 * A223165 A263558 A343092

Adjacent sequences: A264160 A264161 A264162 * A264164 A264165 A264166

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 06 2015

Status

approved