A263519 T(n,k) = Number of (n+1) X (k+1) arrays of permutations of 0..(n+1)*(k+1)-1 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

3, 7, 8, 15, 35, 23, 29, 160, 208, 66, 53, 660, 2076, 1198, 190, 93, 2651, 18369, 25968, 7022, 547, 159, 10350, 158109, 489294, 331130, 41035, 1575, 267, 39807, 1317780, 9051857, 13332096, 4213002, 240237, 4535, 443, 151463, 10791350, 162207955

Offset

1,1

Comments

Table starts

.....3.......7.........15............29...............53..................93

.....8......35........160...........660.............2651...............10350

....23.....208.......2076.........18369...........158109.............1317780

....66....1198......25968........489294..........9051857...........162207955

...190....7022.....331130......13332096........529329240.........20339400914

...547...41035....4213002.....362159570......30867389241.......2543460828164

..1575..240237...53712998....9866744449....1805523575884.....319022980139204

..4535.1406038..684799391..268827612021..105637731091773...40028581755172441

.13058.8230727.8732881192.7327820172316.6184312882582853.5025951440933512579

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

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

k=2: [order 10]

k=3: [order 35]

Empirical for row n:

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

n=2: [order 10]

n=3: [order 29]

n=4: [order 92]

Example

Some solutions for n=3 k=4
..0..1..7..8..9....0..1..7..8..9....0..1..2..3..4....0..1..2..4..9
..6..5..2..3..4...10..5..2..3..4....5..6..8..7..9....5..7..6..3..8
.10.12.11.13.19...11..6.12.13.14...15.10.13.12.14...10.12.11.14.13
.15.17.16.18.14...15.16.17.19.18...16.11.18.17.19...15.16.17.18.19

Crossrefs

Column 1 is A147704(n+1).

Row 1 is A192960.

Sequence in context: A249435 A192120 A031404 * A105263 A242572 A136136

Adjacent sequences: A263516 A263517 A263518 * A263520 A263521 A263522

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 19 2015

Status

approved