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A220547 Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor. 5
2, 8, 29, 108, 401, 1490, 5536, 20569, 76424, 283953, 1055026, 3919944, 14564533, 54114452, 201061985, 747044834, 2775641472, 10312882481, 38317465040, 142368356257, 528968939938, 1965381541064, 7302365621709, 27131904192124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A220553.

LINKS

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

FORMULA

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

Empirical g.f.: x*(1 + x)*(2 - x^2) / (1 - 3*x - 3*x^2 + x^3 + x^4). - Colin Barker, Mar 13 2018

Empirical: a(n) = A000078(2*n + 3). - Greg Dresden, Jan 10 2021

EXAMPLE

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

..8..8....0..7....6..4....6..4....8..0....0..0....0..0....0..0....0..8....6..4

..2..2....3..8....0..0....6..4....2..8....8..8....0..8....0..0....8..2....8..8

..6..4....0..2....0..0....0..0....0..2....2..2....0..2....0..0....2..0....2..2

CROSSREFS

Cf. A220553, A000078.

Sequence in context: A100477 A302266 A011367 * A261774 A345131 A150733

Adjacent sequences:  A220544 A220545 A220546 * A220548 A220549 A220550

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 15 2012

STATUS

approved

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Last modified August 15 15:07 EDT 2022. Contains 356146 sequences. (Running on oeis4.)