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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.

%I A263519 #8 Apr 21 2021 11:45:10
%S A263519 3,7,8,15,35,23,29,160,208,66,53,660,2076,1198,190,93,2651,18369,
%T A263519 25968,7022,547,159,10350,158109,489294,331130,41035,1575,267,39807,
%U A263519 1317780,9051857,13332096,4213002,240237,4535,443,151463,10791350,162207955
%N 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.
%C A263519 Table starts
%C A263519 .....3.......7.........15............29...............53..................93
%C A263519 .....8......35........160...........660.............2651...............10350
%C A263519 ....23.....208.......2076.........18369...........158109.............1317780
%C A263519 ....66....1198......25968........489294..........9051857...........162207955
%C A263519 ...190....7022.....331130......13332096........529329240.........20339400914
%C A263519 ...547...41035....4213002.....362159570......30867389241.......2543460828164
%C A263519 ..1575..240237...53712998....9866744449....1805523575884.....319022980139204
%C A263519 ..4535.1406038..684799391..268827612021..105637731091773...40028581755172441
%C A263519 .13058.8230727.8732881192.7327820172316.6184312882582853.5025951440933512579
%H A263519 R. H. Hardin, <a href="/A263519/b263519.txt">Table of n, a(n) for n = 1..144</a>
%F A263519 Empirical for column k:
%F A263519 k=1: a(n) = 3*a(n-1) -a(n-3)
%F A263519 k=2: [order 10]
%F A263519 k=3: [order 35]
%F A263519 Empirical for row n:
%F A263519 n=1: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4)
%F A263519 n=2: [order 10]
%F A263519 n=3: [order 29]
%F A263519 n=4: [order 92]
%e A263519 Some solutions for n=3 k=4
%e A263519 ..0..1..7..8..9....0..1..7..8..9....0..1..2..3..4....0..1..2..4..9
%e A263519 ..6..5..2..3..4...10..5..2..3..4....5..6..8..7..9....5..7..6..3..8
%e A263519 .10.12.11.13.19...11..6.12.13.14...15.10.13.12.14...10.12.11.14.13
%e A263519 .15.17.16.18.14...15.16.17.19.18...16.11.18.17.19...15.16.17.18.19
%Y A263519 Column 1 is A147704(n+1).
%Y A263519 Row 1 is A192960.
%K A263519 nonn,tabl
%O A263519 1,1
%A A263519 _R. H. Hardin_, Oct 19 2015