A220597 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 3-loops.

1, 7, 65, 471, 3469, 25747, 190425, 1408823, 10424813, 77135267, 570740149, 4223043591, 31247282909, 231205914319, 1710746473929, 12658211881263, 93661059763965, 693020010391803, 5127816575062977, 37941909947454471

Offset

1,2

Comments

Column 3 of A220602.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 7*a(n-2) + 25*a(n-3) - 3*a(n-4) + 9*a(n-5) + 22*a(n-6) - 5*a(n-7) - 2*a(n-8).

Empirical g.f.: x*(1 + x + 16*x^2 + 7*x^3 + 16*x^4 + 23*x^5 - 5*x^6 - 2*x^7) / ((1 - x + x^2)*(1 - 5*x - 13*x^2 - 33*x^3 - 17*x^4 + 7*x^5 + 2*x^6)). - Colin Barker, Aug 01 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):
.68.46.48...00.67.47...00.68.48...00.68.48...00.67.47...68.46.47...00.00.78
.28.68.24...38.36.48...68.24.27...00.27.28...38.38.00...26.34.00...68.34.28
.26.24.00...26.46.24...26.34.00...36.46.24...26.24.00...00.00.00...26.46.24

Crossrefs

Cf. A220602.

Sequence in context: A274823 A174508 A253802 * A264875 A083302 A099342

Adjacent sequences: A220594 A220595 A220596 * A220598 A220599 A220600

Keyword

nonn

Author

R. H. Hardin, Dec 16 2012

Status

approved