proposed

approved

editing

proposed

Number of ways to reciprocally link elements of an nX6 n X 6 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Column 6 of A220708.

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

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

Cf. A220708.

R. H. Hardin , Dec 18 2012

approved

editing

editing

approved

R. H. Hardin, <a href="/A220706/b220706.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links

1, 8, 24, 105, 405, 1617, 6412, 25449, 101029, 400986, 1591697, 6317904, 25077948, 99542634, 395117919, 1568354512, 6225321052, 24710371599, 98083689723, 389326813396, 1545367714146, 6134078853549, 24348200775585, 96646113488531

1,2

Column 6 of A220708

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)

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

allocated

nonn

R. H. Hardin Dec 18 2012

approved

editing

allocated for R. H. Hardin

allocated

approved