A264017 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 1,2 or 2,2.

1, 2, 1, 4, 5, 1, 8, 25, 13, 1, 16, 105, 169, 34, 1, 32, 441, 1573, 1156, 89, 1, 64, 1869, 14641, 20570, 7921, 233, 1, 128, 7921, 146410, 366025, 269225, 54289, 610, 1, 256, 33553, 1464100, 7320500, 9150625, 3524125, 372100, 1597, 1, 512, 142129, 14641000

Offset: 1

Author

R. H. Hardin, Nov 01 2015

Keywords

• nonn
• tabl

Comments

Table starts

.1....2........4..........8............16...............32..................64

.1....5.......25........105...........441.............1869................7921

.1...13......169.......1573.........14641...........146410.............1464100

.1...34.....1156......20570........366025..........7320500...........146410000

.1...89.....7921.....269225.......9150625........398967250.........17394972100

.1..233....54289....3524125.....228765625......21860843125.......2089022169025

.1..610...372100...46131250....5719140625....1201888840625.....252579343635025

.1.1597..2550409..603865625..142978515625...66099082156250...30557658560100100

.1.4181.17480761.7904703125.3574462890625.3635200164062500.3696969485250250000

Examples

			Some solutions for n=4 k=4
..0..8..9..3..4....0.13..2..3..4....7..1.14..3..4....7..1.14..3..4
..5.13.14..1..2...12..6..7..8..9...17..6..0..8..9...12.13..0..8..9
.17.18.12..6..7...22.23.24..1.14...10.11..5.13..2...17.18..5..6..2
.15.16.10.11.19...15.16..5.18.19...15.23.24.18.19...15.16.10.11.19
.20.21.22.23.24...20.21.10.11.17...20.21.22.16.12...20.21.22.23.24
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..143

Crossrefs

Column 2 is A001519(n+1).

Column 3 is A081068.

Row 1 is A000079(n-1).

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 15*a(n-1) -25*a(n-2) for n>4

k=5: a(n) = 25*a(n-1) for n>3

k=6: a(n) = 60*a(n-1) -300*a(n-2) +1500*a(n-3) -7500*a(n-4) +3125*a(n-5) for n>7

k=7: [order 13] for n>15

Empirical for row n:

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

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

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

n=4: a(n) = 19*a(n-1) +304*a(n-3) +256*a(n-4) for n>8

n=5: [order 14] for n>18

n=6: [order 25] for n>31