A264655 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 1,1 2,2 -1,0 or 0,-1.

0, 1, 1, 0, 2, 0, 0, 4, 4, 0, 1, 9, 4, 9, 1, 0, 18, 22, 22, 18, 0, 0, 41, 65, 112, 65, 41, 0, 1, 84, 193, 716, 716, 193, 84, 1, 0, 176, 628, 3100, 6656, 3100, 628, 176, 0, 0, 369, 1905, 14871, 48781, 48781, 14871, 1905, 369, 0, 1, 772, 5929, 73900, 406871, 580796

Offset

1,5

Comments

Table starts

.0...1.....0.......0.........1...........0.............0..............1

.1...2.....4.......9........18..........41............84............176

.0...4.....4......22........65.........193...........628...........1905

.0...9....22.....112.......716........3100.........14871..........73900

.1..18....65.....716......6656.......48781........406871........3133028

.0..41...193....3100.....48781......580796.......7644038.......93971260

.0..84...628...14871....406871.....7644038.....159104356.....3198623964

.1.176..1905...73900...3133028....93971260....3198623964...100746278612

.0.369..5929..349328..24130345..1163775908...62394318265..3118543214377

.0.772.18406.1679736.189393503.14482108589.1226341881232.98267901838019

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-5) -2*a(n-6) +4*a(n-7) -a(n-10)

k=3: [order 15]

k=4: [order 18] for n>21

Example

Some solutions for n=4 k=4
..1..6..7..4..9....1..2..3..4..9....5..2..3..4..9....1..2..7..4..9
.10.11..8..2..3...10..7..8.13.14...10..0..1.13.14....6.11.12.13..3
.15.16..0.14.19...15.16..0.18.19...11.16..6.18..8...15.16..0.14..8
.20.17..5.12.13...20.17..5..6.24...20.17.22.19..7...20.10..5.19.24
.21.22.23.24.18...21.22.23.11.12...21.15.23.24.12...21.22.23.17.18

Crossrefs

Sequence in context: A072070 A137830 A137828 * A264476 A342276 A137505

Adjacent sequences: A264652 A264653 A264654 * A264656 A264657 A264658

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 20 2015

Status

approved