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 A220616 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor. 1
 3, 21, 125, 765, 4657, 28373, 172833, 1052829, 6413369, 39067429, 237981569, 1449678893, 8830805161, 53793374581, 327685538769, 1996115937021, 12159458878905, 74070066514885, 451202212873441, 2748525099013581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 3 of A220621. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = 7*a(n-1) - 4*a(n-2) - 10*a(n-3) + 4*a(n-4). Empirical g.f.: x*(1 + 2*x)*(3 - 6*x + 2*x^2) / (1 - 7*x + 4*x^2 + 10*x^3 - 4*x^4). - 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): ..0..6..4....0..7..0....0..7..0....0..0..0....6..4..0....0..6..4....0..9..7 ..0..6..4....3..6..4....3..7..7....0..9..7....0..7..0....6..4..0....0..3..1 ..0..0..0....0..6..4....3..3..0....0..3..1....3..0..0....6..4..0....6..4..0 CROSSREFS Cf. A220621. Sequence in context: A004658 A034552 A356889 * A273803 A036754 A121447 Adjacent sequences: A220613 A220614 A220615 * A220617 A220618 A220619 KEYWORD nonn AUTHOR R. H. Hardin, Dec 17 2012 STATUS approved

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Last modified September 28 16:15 EDT 2023. Contains 365736 sequences. (Running on oeis4.)