A264090 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 0,1 or 2,-2.

4, 9, 8, 25, 39, 16, 64, 245, 169, 32, 169, 1448, 2401, 715, 64, 441, 8788, 32761, 24010, 3025, 128, 1156, 52941, 456976, 645627, 240100, 12815, 256, 3025, 319906, 6355441, 19553300, 12723489, 2401000, 54289, 512, 7921, 1931215, 88529281, 563080476

Offset

1,1

Comments

Table starts

...4.....9.......25.........64...........169.............441...............1156

...8....39......245.......1448..........8788...........52941.............319906

..16...169.....2401......32761........456976.........6355441...........88529281

..32...715....24010.....645627......19553300.......563080476........16552783250

..64..3025...240100...12723489.....836655625.....49887902736......3094960562500

.128.12815..2401000..252076323...35960283125...4553473226652....607571415109250

.256.54289.24010000.4994107561.1545608400625.415614152704689.119272286997956401

Links

R. H. Hardin, Table of n, a(n) for n = 1..198

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 19*a(n-1) +304*a(n-3) +256*a(n-4)

k=5: [order 14]

k=6: [order 25] for n>27

k=7: [order 25] for n>27

Empirical for row n:

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

n=2: [order 8]

n=3: a(n) = 14*a(n-1) +14*a(n-2) -210*a(n-3) +210*a(n-5) -14*a(n-6) -14*a(n-7) +a(n-8)

n=4: [order 52]

n=5: [order 96]

Example

Some solutions for n=3 k=4
..0..1..2.11..3....1..0.10.11..4....0..1..2..4..3....1..0..3..2..4
..6..5..7..9..8....5..7..6.16..9....5..6..8.16.17....5..6.15..8.17
.10.12..4.14.13....2..3.12.13.14...11.10.13.12.14...11.10.12.13.14
.15.16.17.19.18...15..8.18.17.19....7.15..9.19.18....7.16..9.19.18

Crossrefs

Column 1 is A000079(n+1).

Row 1 is A007598(n+2).

Sequence in context: A064549 A304203 A087687 * A345283 A369750 A365780

Adjacent sequences: A264087 A264088 A264089 * A264091 A264092 A264093

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2015

Status

approved