A220720 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors.

1, 7, 30, 126, 534, 2275, 9667, 41089, 174660, 742428, 3155820, 13414405, 57020437, 242375995, 1030264362, 4379330826, 18615162402, 79127219431, 336345003127, 1429697162869, 6077194423824, 25832248272072, 109804788896376

Offset

1,2

Comments

Column 3 of A220725.

Links

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

Formula

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

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

Example

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
.69.49.00...69.47.00...00.00.00...00.79.00...69.47.00...00.69.47...00.79.00
.00.17.17...39.16.47...00.69.47...39.69.14...39.19.00...00.36.14...36.49.17
.36.34.00...00.13.00...00.36.14...00.16.14...00.16.14...00.00.00...00.36.14

Crossrefs

Cf. A220725.

Sequence in context: A037611 A171472 A369201 * A024311 A210100 A297080

Adjacent sequences: A220717 A220718 A220719 * A220721 A220722 A220723

Keyword

nonn

Author

R. H. Hardin, Dec 18 2012

Status

approved