A263519 - OEIS

%I #8 Apr 21 2021 11:45:10

%S 3,7,8,15,35,23,29,160,208,66,53,660,2076,1198,190,93,2651,18369,

%T 25968,7022,547,159,10350,158109,489294,331130,41035,1575,267,39807,

%U 1317780,9051857,13332096,4213002,240237,4535,443,151463,10791350,162207955

%N 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.

%C Table starts

%C .....3.......7.........15............29...............53..................93

%C .....8......35........160...........660.............2651...............10350

%C ....23.....208.......2076.........18369...........158109.............1317780

%C ....66....1198......25968........489294..........9051857...........162207955

%C ...190....7022.....331130......13332096........529329240.........20339400914

%C ...547...41035....4213002.....362159570......30867389241.......2543460828164

%C ..1575..240237...53712998....9866744449....1805523575884.....319022980139204

%C ..4535.1406038..684799391..268827612021..105637731091773...40028581755172441

%C .13058.8230727.8732881192.7327820172316.6184312882582853.5025951440933512579

%H R. H. Hardin, <a href="/A263519/b263519.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

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

%F k=2: [order 10]

%F k=3: [order 35]

%F Empirical for row n:

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

%F n=2: [order 10]

%F n=3: [order 29]

%F n=4: [order 92]

%e Some solutions for n=3 k=4

%e ..0..1..7..8..9....0..1..7..8..9....0..1..2..3..4....0..1..2..4..9

%e ..6..5..2..3..4...10..5..2..3..4....5..6..8..7..9....5..7..6..3..8

%e .10.12.11.13.19...11..6.12.13.14...15.10.13.12.14...10.12.11.14.13

%e .15.17.16.18.14...15.16.17.19.18...16.11.18.17.19...15.16.17.18.19

%Y Column 1 is A147704(n+1).

%Y Row 1 is A192960.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 19 2015