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

Author

R. H. Hardin, Oct 19 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A147704(n+1).

Row 1 is A192960.

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]