A220710 Number of ways to reciprocally link elements of an 5 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

1, 1, 8, 28, 107, 405, 1520, 5706, 21418, 80390, 301736, 1132543, 4250895, 15955408, 59887275, 224782132, 843701335, 3166765105, 11886195940, 44613876758, 167454575870, 628527215306, 2359126067724, 8854788952291, 33235734276043

Offset: 1

Author

R. H. Hardin, Dec 18 2012

Keywords

• nonn

Comments

Row 5 of A220708.

Examples

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.00...00.00.00...00.67.47...00.67.47...00.00.00...00.00.00...00.00.00
.00.67.47...00.00.00...36.34.00...36.34.00...00.00.00...00.67.47...00.00.00
.36.34.00...00.00.00...00.00.00...00.00.00...00.67.47...36.34.00...00.00.00
.00.00.00...00.67.47...00.00.00...00.67.47...36.34.00...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00...36.34.00...00.00.00...36.34.00...00.00.00
		

Links

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

Crossrefs

Cf. A220708.

Formula

Empirical: a(n) = 3*a(n-1) + 7*a(n-2) - 14*a(n-3) - 11*a(n-4) + 17*a(n-5) + 5*a(n-6) - 6*a(n-7) for n>11.

Empirical g.f.: x*(1 - 2*x - 2*x^2 + 11*x^3 - 8*x^4 - 6*x^5 + 14*x^6 - 18*x^7 - 3*x^8 + 18*x^9 - 8*x^10) / ((1 - x)*(1 + x)*(1 - 3*x - 6*x^2 + 11*x^3 + 5*x^4 - 6*x^5)). - Colin Barker, Aug 02 2018