A220676 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links.

1, 9, 43, 201, 968, 4604, 22000, 104976, 501096, 2391737, 11415981, 54489429, 260082487, 1241395361, 5925282424, 28281863304, 134991671188, 644326407852, 3075423213984, 14679249263905, 70065270353385, 334427328092001

Offset

1,2

Comments

Column 3 of A220681.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 11*a(n-2) + 10*a(n-3) + 2*a(n-4) + 5*a(n-5) + 4*a(n-6) - a(n-7).

Empirical g.f.: x*(1 + 7*x + 14*x^2 + 6*x^3 + x^4 + 4*x^5 - x^6) / ((1 + x)*(1 - 3*x - 8*x^2 - 2*x^3 - 5*x^5 + x^6)). - Colin Barker, Aug 02 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):
.00.00.00...00.67.48...68.47.00...68.47.00...00.78.00...68.48.00...00.00.00
.00.68.47...38.68.24...23.78.00...23.68.47...38.27.78...26.24.00...68.48.00
.00.23.00...26.24.00...36.24.00...00.23.00...23.36.24...00.00.00...26.24.00

Crossrefs

Cf. A220681.

Sequence in context: A259181 A330088 A281773 * A110125 A221751 A275793

Adjacent sequences: A220673 A220674 A220675 * A220677 A220678 A220679

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved