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A220706 Number of ways to reciprocally link elements of an n X 6 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links. 1
1, 8, 24, 105, 405, 1617, 6412, 25449, 101029, 400986, 1591697, 6317904, 25077948, 99542634, 395117919, 1568354512, 6225321052, 24710371599, 98083689723, 389326813396, 1545367714146, 6134078853549, 24348200775585, 96646113488531 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 6 of A220708.

LINKS

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

FORMULA

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 3*a(n-3) - 6*a(n-4) - a(n-5) - a(n-6) + 4*a(n-7) + a(n-8) - a(n-9) - a(n-10).

Empirical g.f.: x*(1 + x)*(1 + 4*x - 9*x^2 + 5*x^3 - 5*x^4 + 3*x^5 + x^6 - x^8) / (1 - 3*x - 5*x^2 + 3*x^3 + 6*x^4 + x^5 + x^6 - 4*x^7 - x^8 + x^9 + x^10). - Colin Barker, Aug 02 2018

EXAMPLE

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

.00.00.67.47.67.47...00.00.00.00.67.47...00.00.00.00.00.00...00.00.00.00.00.00

.00.36.34.36.34.00...00.67.47.36.34.00...00.00.67.47.67.47...00.00.00.00.00.00

.00.00.00.00.00.00...36.34.00.00.00.00...00.36.34.36.34.00...00.00.00.00.00.00

CROSSREFS

Cf. A220708.

Sequence in context: A281463 A267326 A063515 * A246030 A010566 A305224

Adjacent sequences:  A220703 A220704 A220705 * A220707 A220708 A220709

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 18 2012

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)