A220622 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor

1, 22, 125, 1189, 9176, 76955, 624227, 5131406, 41957895, 343809419, 2814822600, 23053276257, 188779537161, 1545969533334, 12660108907789, 103675885828389, 849017313171328, 6952739324271787, 56937068599653211, 466266655043137726

Offset

1,2

Comments

Row 3 of A220621.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 22*a(n-2) - 32*a(n-3) - 12*a(n-4) + 8*a(n-5) - 3*a(n-6).

Empirical g.f.: x*(1 + 16*x - 29*x^2 - 13*x^3 + 8*x^4 - 3*x^5) / (1 - 6*x - 22*x^2 + 32*x^3 + 12*x^4 - 8*x^5 + 3*x^6). - Colin Barker, Aug 01 2018

Example

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
..6..4..0....0..6..4....0..7..0....0..0..0....6..4..0....0..7..0....0..7..0
..0..0..0....0..6..4....3..6..4....0..0..0....9..9..0....3..6..4....3..0..7
..0..0..0....6..4..0....0..6..4....0..6..4....0..1..1....0..0..0....0..3..0

Crossrefs

Cf. A220621.

Sequence in context: A209736 A209729 A252835 * A229375 A309923 A215626

Adjacent sequences: A220619 A220620 A220621 * A220623 A220624 A220625

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved