A263520 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.

8, 35, 160, 660, 2651, 10350, 39807, 151463, 572454, 2153977, 8081566, 30264786, 113201857, 423085492, 1580453125, 5901900685, 22034817900, 82255893847, 307033492332, 1145986101448, 4277171754383, 15963330711354, 59577671664211

Offset: 1

Author

R. H. Hardin, Oct 19 2015

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..1..2..8..9....0..1..2..4..9....0..1..2..3..4....0..2..3..4..9
.10..5..7..3..4....5..6..8..3.14....5..6.12..7.14....5..1..6..7..8
.11..6.12.14.13...11.10..7.12.13...11.10.13..8..9...10.11.13.12.14
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Row 2 of A263519.

Formula

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).

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