A264195 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 0,2 or 2,1.

1, 4, 2, 16, 18, 4, 36, 180, 81, 8, 81, 864, 2025, 360, 16, 225, 4608, 20736, 19845, 1600, 32, 625, 29040, 262144, 395280, 194481, 6760, 64, 1600, 184525, 3748096, 10764800, 7535025, 1944810, 28561, 128, 4096, 1089000, 54479161, 324210304, 442050625

Offset: 1

Author

R. H. Hardin, Nov 07 2015

Keywords

• nonn
• tabl

Comments

Table starts

..1.....4.......16.........36...........81.............225.............625

..2....18......180........864.........4608...........29040..........184525

..4....81.....2025......20736.......262144.........3748096........54479161

..8...360....19845.....395280.....10764800.......324210304......9863496016

.16..1600...194481....7535025....442050625.....28044191296...1785793904896

.32..6760..1944810..150305220..19169627850...2585148634024.357076938417216

.64.28561.19448100.2998219536.831295356516.238302234835681

Examples

			Some solutions for n=3 k=4
..2..1.13..3..4...11..1.13..3..4...11..1.13.14..4....0.12..2.14..4
..5.17..7..6..9....5..6..9.19..7....5..6..9.19..7....7..6..5..8..9
.10..0.14.11.12...10..0.14..2.12...12..0.10..2..3...10.13..1.11..3
.15.16.19.18..8...15.18.17.16..8...15.16.17.18..8...17.18.15.16.19
		

Links

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

Crossrefs

Column 1 is A000079(n-1).

Row 1 is A189145(n+1).

Formula

Empirical for column k:

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

k=2: [order 14]

k=3: a(n) = 10*a(n-1) for n>5

k=4: [order 14] for n>16

k=5: [order 58]

Empirical for row n:

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

n=2: [order 44]

n=3: [order 30]