A264628 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 -2,0 -1,0 0,-1 or 1,1.

0, 1, 1, 0, 2, 2, 0, 4, 4, 1, 1, 9, 13, 8, 1, 0, 16, 40, 22, 16, 4, 0, 37, 125, 108, 61, 32, 6, 1, 76, 393, 684, 660, 280, 64, 5, 0, 160, 1200, 2736, 6107, 4032, 832, 128, 7, 0, 337, 3759, 13556, 37225, 50353, 19521, 2373, 256, 15, 1, 704, 11572, 68972, 349391, 604916

Offset: 1

Author

R. H. Hardin, Nov 19 2015

Keywords

• nonn
• tabl

Comments

Table starts

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

..1...2.....4.......9........16..........37............76............160

..2...4....13......40.......125.........393..........1200...........3759

..1...8....22.....108.......684........2736.........13556..........68972

..1..16....61.....660......6107.......37225........349391........2557552

..4..32...280....4032.....50353......604916.......7907841.......93847752

..6..64...832...19521....389512.....7201068.....145801320.....2894056084

..5.128..2373...89469...2986345....81028312....2739867178....84594500932

..7.256..7225..449550..23242594...992539392...54011094032..2549159514025

.15.512.24371.2308554.180618759.12531858912.1041910674136.78013734570966

Examples

			Some solutions for n=4 k=4
..5.11..7..4..9....5..2..7..4.14....1..6..7..4..9....1..2..7..4.14
..6..0..1..2..3....6..0..1..9..3...10..0.12..2..3....6..0.12..9..3
.20.12.13.14..8...15.12.13.23..8...20..5.22.14..8...11..5.13.23..8
.16.10.22.19.24...20.10.11.19.24...16.17.11.19.13...20.10.22.19.24
.21.15.23.17.18...21.22.16.17.18...21.15.23.24.18...21.15.16.17.18
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..162

Crossrefs

Column 2 is A000079(n-1).

Formula

Empirical for column k:

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

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

k=3: [order 45]

k=4: [order 11] for n>12

Empirical for row n:

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

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

n=3: [order 15]

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