A220705 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

1, 5, 12, 37, 107, 317, 932, 2749, 8101, 23881, 70392, 207497, 611639, 1802937, 5314536, 15665721, 46178025, 136119501, 401241028, 1182742829, 3486384739, 10276856693, 30293209548, 89295644789, 263217806797, 775890178961

Offset

1,2

Comments

Column 5 of A220708.

Links

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

Formula

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

Empirical g.f.: x*(1 + 3*x - x^2 - 2*x^3 - 2*x^4 - x^5) / ((1 - x)*(1 + x)*(1 - 2*x - 2*x^2 - 2*x^3 - x^4)). - 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):
.00.00.67.47.00...00.00.00.00.00...00.00.00.00.00...00.67.47.00.00
.00.36.34.67.47...00.67.47.67.47...00.00.00.00.00...36.34.00.00.00
.00.00.36.34.00...36.34.36.34.00...00.00.00.00.00...00.00.00.00.00

Crossrefs

Cf. A220708.

Sequence in context: A300534 A359189 A297909 * A034752 A095310 A122299

Adjacent sequences: A220702 A220703 A220704 * A220706 A220707 A220708

Keyword

nonn

Author

R. H. Hardin, Dec 18 2012

Status

approved