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A220633 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors. 1
1, 1, 3, 12, 44, 158, 564, 2010, 7160, 25502, 90828, 323490, 1152128, 4103366, 14614356, 52049802, 185378120, 660233966, 2351458140, 8374842354, 29827443344, 106232014742, 378350930916, 1347516822234, 4799252328536, 17092790630078 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 3 of A220632.

LINKS

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

FORMULA

Empirical: a(n) = 4*a(n-1) - a(n-2) - 2*a(n-3) for n>5.

Empirical g.f.: x*(1 - x - x^2)*(1 - 2*x - x^2) / ((1 - x)*(1 - 3*x - 2*x^2)). - Colin Barker, Aug 02 2018

EXAMPLE

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

.00.00.00...00.67.47...00.00.00

.00.67.47...36.34.00...00.00.00

.36.34.00...00.00.00...00.00.00

CROSSREFS

Cf. A220632.

Sequence in context: A282082 A167477 A190051 * A296225 A109437 A331473

Adjacent sequences:  A220630 A220631 A220632 * A220634 A220635 A220636

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 17 2012

STATUS

approved

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Last modified May 16 12:46 EDT 2021. Contains 343947 sequences. (Running on oeis4.)