A264649 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 1,1 2,2 -1,0 or 0,-1.

1, 2, 4, 9, 18, 41, 84, 176, 369, 772, 1625, 3406, 7156, 15025, 31542, 66225, 139016, 291856, 612705, 1286296, 2700433, 5669210, 11901844, 24986425, 52455914, 110124697, 231193116, 485361376, 1018956049, 2139172156, 4490927145

Offset

1,2

Links

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

Formula

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

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

Example

Some solutions for n=4:
..1..2..5....1..2..5....3..2..5....3..2..5....3..2..5....1..2..5....1..2..5
..4..7..8....4..0..8....4..0..1....6..0..1....6..0..1....6..0..8....6..0..8
..9.10..0....7..3.11....9..8.11....7..8..4....9..8..4....7..3..4....9..3..4
.12.11..3...12..6.14...12..6..7...12.11.14...12.11..7...12.11.14...12.11..7
.13.14..6...13..9.10...13.14.10...13..9.10...13.14.10...13..9.10...13.14.10

Crossrefs

Column 2 of A264655.

Sequence in context: A171003 A094291 A026765 * A259803 A032175 A000678

Adjacent sequences: A264646 A264647 A264648 * A264650 A264651 A264652

Keyword

nonn

Author

R. H. Hardin, Nov 20 2015

Status

approved