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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
1, 22, 125, 1189, 9176, 76955, 624227, 5131406, 41957895, 343809419, 2814822600, 23053276257, 188779537161, 1545969533334, 12660108907789, 103675885828389, 849017313171328, 6952739324271787, 56937068599653211, 466266655043137726 (list; graph; refs; listen; history; text; internal format)
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 A206418 A309923

Adjacent sequences:  A220619 A220620 A220621 * A220623 A220624 A220625

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 17 2012

STATUS

approved

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Last modified February 25 14:40 EST 2021. Contains 341609 sequences. (Running on oeis4.)