A220564 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal or antidiagonal neighbor.

1, 13, 64, 430, 2604, 16310, 101052, 628269, 3901815, 24240377, 150578968, 935414825, 5810847665, 36097422853, 224239670624, 1392992694942, 8653368270212, 53755331997318, 333931897912068, 2074408410086741

Offset

1,2

Comments

Row 3 of A220562.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 15*a(n-2) - 5*a(n-3) - 19*a(n-4) + 9*a(n-5) + 2*a(n-6) - a(n-7).

Empirical g.f.: x*(1 - x)*(1 + 10*x + 7*x^2 - 9*x^3 - x^4 + x^5) / ((1 + x - x^2)*(1 - 5*x - 9*x^2 + 9*x^3 + x^4 - x^5)). - Colin Barker, Aug 01 2018

Example

Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
..0..6..4....6..4..0....0..7..0....0..7..7....0..6..4....6..4..7....0..0..0
..6..4..0....0..7..0....3..0..0....3..3..7....0..0..0....0..3..7....6..4..0
..0..6..4....3..0..0....6..4..0....0..3..0....0..0..0....0..3..0....0..6..4

Crossrefs

Cf. A220562.

Sequence in context: A166605 A054477 A169883 * A264513 A302161 A302633

Adjacent sequences: A220561 A220562 A220563 * A220565 A220566 A220567

Keyword

nonn

Author

R. H. Hardin, Dec 16 2012

Status

approved