A264670 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

1, 2, 9, 19, 44, 108, 264, 649, 1573, 3837, 9353, 22801, 55571, 135432, 330113, 804604, 1961113, 4779902, 11650318, 28396001, 69211142, 168692149, 411162676, 1002149647, 2442594935, 5953472042, 14510727488, 35367800720, 86203902041

Offset

1,2

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-3) + 3*a(n-4) + 2*a(n-5) - a(n-6) + 4*a(n-7) - a(n-8) - a(n-10).

Empirical g.f.: x*(1 + 5*x^2 + x^4 + 3*x^5 - x^6 - x^8) / (1 - 2*x - x^3 - 3*x^4 - 2*x^5 + x^6 - 4*x^7 + x^8 + x^10). - Colin Barker, Jan 08 2019

Example

Some solutions for n=4:
..5..0..1....4..0..1....5..0..1....4..0..1....4..0..1....5..0..1....8..0..1
.11..3..2...11..8..2....8..3..2....8..3..2....7..8..2...11..8..2...11..3..2
.10..4..7....3..6..5...11..4..7...14.11..5....3..6..5....3..4..7...14..4..5
..6.14..8...14..7.10....6.14.10....6..7.10...13.14.10....6.14.10....6..7.10
..9.12.13....9.12.13....9.12.13....9.12.13....9.12.11....9.12.13....9.12.13

Crossrefs

Column 2 of A264676.

Sequence in context: A294546 A135207 A274853 * A026541 A038249 A116014

Adjacent sequences: A264667 A264668 A264669 * A264671 A264672 A264673

Keyword

nonn

Author

R. H. Hardin, Nov 20 2015

Status

approved