A264294 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,1 0,-2 1,0 or -1,0.

2, 9, 20, 56, 169, 441, 1258, 3520, 9701, 27216, 75725, 210743, 588040, 1637433, 4562629, 12715864, 35425613, 98714880, 275062034, 766408103, 2135548297, 5950451808, 16580224900, 46199140975, 128728625258, 358688168631

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 5*a(n-3) - 5*a(n-4) - 5*a(n-5) + 4*a(n-6) - a(n-7) - a(n-8).

Empirical g.f.: x*(1 - x)*(2 + 9*x + 12*x^2 + 2*x^3 + 3*x^5 + x^6) / (1 - x - 4*x^2 - 5*x^3 + 5*x^4 + 5*x^5 - 4*x^6 + x^7 + x^8). - Colin Barker, Jan 07 2019

Example

Some solutions for n=4:
..2..4..5....2..4..5....2..4..1....2..0..1....2..0..1....3..4..5....2..0..1
..0..1..8....0..1..8....0..3..8....5..3..4....6..7..8....0..1..2....5..3..4
..3..6.11....3.10.11....9..6..5....8.10..7....3..4..5....8..6..7....9.10.11
.12..7.14....6..7.14...11..7.10....6.13.14...12.13.14...11..9.10....6..7..8
..9.10.13....9.12.13...14.12.13....9.12.11....9.10.11...14.12.13...14.12.13

Crossrefs

Column 2 of A264299.

Sequence in context: A272211 A259035 A093835 * A280295 A041007 A002360

Adjacent sequences: A264291 A264292 A264293 * A264295 A264296 A264297

Keyword

nonn

Author

R. H. Hardin, Nov 11 2015

Status

approved