A263989 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 or 1,2.

1, 2, 1, 4, 4, 1, 8, 16, 8, 1, 16, 48, 64, 16, 1, 32, 144, 288, 256, 32, 1, 64, 432, 1296, 1728, 1024, 64, 1, 128, 1296, 6480, 11664, 10368, 4096, 128, 1, 256, 3888, 32400, 97200, 104976, 62208, 16384, 256, 1, 512, 11664, 162000, 810000, 1458000, 944784, 373248

Offset

1,2

Comments

Table starts

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

.1....4......16.......48........144...........432............1296

.1....8......64......288.......1296..........6480...........32400

.1...16.....256.....1728......11664.........97200..........810000

.1...32....1024....10368.....104976.......1458000........20250000

.1...64....4096....62208.....944784......21870000.......506250000

.1..128...16384...373248....8503056.....328050000.....12656250000

.1..256...65536..2239488...76527504....4920750000....316406250000

.1..512..262144.13436928..688747536...73811250000...7910156250000

.1.1024.1048576.80621568.6198727824.1107168750000.197753906250000

Links

R. H. Hardin, Table of n, a(n) for n = 1..479

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 6*a(n-1)

k=5: a(n) = 9*a(n-1)

k=6: a(n) = 15*a(n-1) for n>2

k=7: a(n) = 25*a(n-1) for n>2

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) for n>3

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

n=4: a(n) = 8*a(n-1) for n>7

n=5: a(n) = 13*a(n-1) for n>9

n=6: a(n) = 21*a(n-1) for n>11

n=7: a(n) = 34*a(n-1) for n>13

Example

Some solutions for n=4 k=4
..7..8..9..3..4....0..8..2..3..4....0..1..2..3..4....0..1..9..3..4
..5..6..0..1..2...12.13.14..1..9...12..6..7..8..9....5..6..7..8..2
.17.18.12.13.14...10.11..5..6..7...10.18..5.13.14...10.18.19.13.14
.15.16.10.11.19...22.16.17.18.19...22.23.24.11.19...15.16.17.11.12
.20.21.22.23.24...20.21.15.23.24...20.21.15.16.17...20.21.22.23.24

Crossrefs

Column 2 is A000079.

Column 3 is A000302.

Row 1 is A000079(n-1).

Sequence in context: A038207 A113988 A209240 * A202710 A200965 A117427

Adjacent sequences: A263986 A263987 A263988 * A263990 A263991 A263992

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 31 2015

Status

approved