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Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.
1

%I #10 Jan 01 2019 20:13:52

%S 8,35,160,660,2651,10350,39807,151463,572454,2153977,8081566,30264786,

%T 113201857,423085492,1580453125,5901900685,22034817900,82255893847,

%U 307033492332,1145986101448,4277171754383,15963330711354,59577671664211

%N Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

%H R. H. Hardin, <a href="/A263520/b263520.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 11*a(n-2) - 14*a(n-3) + 36*a(n-4) + 8*a(n-5) - 36*a(n-6) - 2*a(n-7) + 13*a(n-8) + a(n-9) - a(n-10).

%F Empirical g.f.: x*(8 - 21*x + 3*x^2 + 37*x^3 - 7*x^4 - 31*x^5 + 6*x^6 + 14*x^7 - x^9) / ((1 - x)^2*(1 + x)^2*(1 - 4*x + x^2)*(1 - x - x^2)*(1 - 2*x - x^2)). - _Colin Barker_, Jan 01 2019

%e Some solutions for n=4:

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

%e .10..5..7..3..4....5..6..8..3.14....5..6.12..7.14....5..1..6..7..8

%e .11..6.12.14.13...11.10..7.12.13...11.10.13..8..9...10.11.13.12.14

%Y Row 2 of A263519.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 19 2015