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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. 1
3, 29, 224, 1814, 14556, 117022, 940432, 7558245, 60744605, 488197825, 3923590632, 31533457665, 253430854415, 2036795298237, 16369494914388, 131559791031398, 1057331255850916, 8497652480629342, 68294678022457540, 548876652325439237 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 13 14:01 EDT 2022. Contains 356091 sequences. (Running on oeis4.)