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

1,1

Links

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

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

Example

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

Crossrefs

Row 2 of A263519.

Sequence in context: A320405 A279379 A098999 * A223901 A192257 A297609

Adjacent sequences: A263517 A263518 A263519 * A263521 A263522 A263523

Keyword

nonn

Author

R. H. Hardin, Oct 19 2015

Status

approved