A264238 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 1,1 0,-1 -1,1 or 0,-2.

8, 21, 89, 296, 1105, 3897, 14128, 50533, 181937, 652944, 2346977, 8429681, 30288280, 108807669, 390915337, 1404388408, 5045461169, 18126337449, 65121053504, 233954670533, 840509324641, 3019625618976, 10848352515265

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - a(n-3).

Empirical g.f.: x*(8 + 5*x - x^2) / (1 - 2*x - 6*x^2 + x^3). - Colin Barker, Jan 06 2019

Example

Some solutions for n=4:
..2..3..4....0..1..2....0..1..2....1..2..4....2..3..4....1..3..2....2..1..4
..5..0..1....3..4..5....3..6..5....5..0..7....5..0..1....4..0..5....5..0..7
..6..7..8....6..8.10....8..9..4....6..3..8....6..8.10....8..9.10....6..3..8
.10.12.11...11.12..7...11.10..7...10.11.13...11.12..7...11..6..7....9.10.11
.13..9.14...13..9.14...12.13.14...12..9.14...13..9.14...12.13.14...12.13.14

Crossrefs

Column 2 of A264244.

Sequence in context: A225658 A226313 A275185 * A188700 A054855 A220611

Adjacent sequences: A264235 A264236 A264237 * A264239 A264240 A264241

Keyword

nonn

Author

R. H. Hardin, Nov 09 2015

Status

approved