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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
OFFSET
1,2
COMMENTS
Column 6 of A220708.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 18 2012
STATUS
approved