A220726 Number of ways to reciprocally link elements of a 2 X n array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors.

1, 2, 7, 21, 68, 221, 717, 2330, 7571, 24601, 79940, 259761, 844081, 2742802, 8912607, 28961101, 94107748, 305798741, 993678757, 3228912810, 10492201691, 34093920401, 110786605380, 359995910921, 1169789934761, 3801177874402

Offset

1,2

Comments

Row 2 of A220725.

Links

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

Formula

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

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

Example

All solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
.00.00.00...00.67.47...69.49.00...00.69.47...69.47.00...69.46.47...00.79.00
.00.00.00...36.34.00...00.16.14...00.36.14...36.14.00...00.13.00...36.46.14

Crossrefs

Cf. A220725.

Sequence in context: A186240 A274203 A330058 * A347302 A127540 A339041

Adjacent sequences: A220723 A220724 A220725 * A220727 A220728 A220729

Keyword

nonn

Author

R. H. Hardin, Dec 18 2012

Status

approved