A264166 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

1, 4, 8, 16, 33, 69, 145, 300, 624, 1300, 2705, 5629, 11713, 24376, 50728, 105564, 219681, 457161, 951361, 1979800, 4120000, 8573800, 17842241, 37130041, 77268321, 160796844, 334621288, 696353256, 1449124353, 3015655309, 6275635985

Offset

1,2

Comments

Column 1 of A264172.

Links

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

Formula

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

Empirical g.f.: x*(1 + x)*(1 + 2*x + x^2 + x^3 - x^4) / ((1 + x^2)*(1 - x - 2*x^2 - x^3 + x^4)). - Colin Barker, Feb 25 2018

Example

Some solutions for n=4:
..5..1....0..1....0..1....0..1....5..0....0..1....5..0....5..1....5..0....0..1
..0..2....2..3....7..3....7..2....2..1....7..3....7..1....0..3....2..1....2..3
..4..3....9..5....2..4....9..3....4..3....2..5....2..3....2..4....9..3....4..5
..6..7....4..7....6..5....4..5....6..7....4..6....4..6....6..7....4..7....6..7
..8..9....6..8....8..9....6..8....8..9....8..9....8..9....8..9....6..8....8..9

Crossrefs

Cf. A264172.

Sequence in context: A068890 A073856 A019458 * A330913 A215346 A214035

Adjacent sequences: A264163 A264164 A264165 * A264167 A264168 A264169

Keyword

nonn

Author

R. H. Hardin, Nov 06 2015

Status

approved