A220709 Number of ways to reciprocally link elements of a 4 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

1, 1, 5, 13, 37, 105, 298, 846, 2404, 6826, 19394, 55081, 156473, 444445, 1262497, 3586113, 10186570, 28935186, 82191652, 233468038, 663174914, 1883771569, 5350922525, 15199487245, 43174696525, 122639283705, 348361331050

Offset: 1

Author

R. H. Hardin, Dec 18 2012

Keywords

• nonn

Comments

Row 4 of A220708.

Examples

			All 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
.00.67.47...00.00.00...36.34.00...36.34.00...00.00.00
.36.34.00...00.00.00...00.00.00...00.67.47...00.67.47
.00.00.00...00.00.00...00.00.00...36.34.00...36.34.00
		

Links

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

Crossrefs

Cf. A220708.

Formula

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

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