A220548 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

3, 29, 224, 1814, 14556, 117022, 940432, 7558245, 60744605, 488197825, 3923590632, 31533457665, 253430854415, 2036795298237, 16369494914388, 131559791031398, 1057331255850916, 8497652480629342, 68294678022457540, 548876652325439237

Offset

1,1

Comments

Column 3 of A220553.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 17*a(n-2) - 3*a(n-3) - 17*a(n-4) + 3*a(n-5) + 4*a(n-6) - a(n-7).

Empirical g.f.: x*(3 + 11*x - x^2 - 14*x^3 + 2*x^4 + 4*x^5 - x^6) / ((1 + x - x^2)*(1 - 7*x - 9*x^2 + 5*x^3 + 3*x^4 - x^5)). - Colin Barker, Jul 31 2018

Example

Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
..0..7..7....0..0..0....0..8..8....8..0..0....8..6..4....6..4..7....0..0..7
..3..3..0....8..6..4....8..2..2....2..0..8....2..6..4....0..3..7....8..3..7
..0..0..0....2..6..4....2..0..0....6..4..2....0..6..4....0..3..0....2..3..0

Crossrefs

Cf. A220553.

Sequence in context: A126185 A083092 A174419 * A153825 A201490 A354402

Adjacent sequences: A220545 A220546 A220547 * A220549 A220550 A220551

Keyword

nonn

Author

R. H. Hardin, Dec 15 2012

Status

approved