A220739 Number of ways to reciprocally link elements of an 2 X n array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links.

1, 2, 5, 13, 32, 85, 221, 578, 1513, 3961, 10368, 27145, 71065, 186050, 487085, 1275205, 3338528, 8740381, 22882613, 59907458, 156839761, 410611825, 1074995712, 2814375313, 7368130225, 19290015362, 50501915861, 132215732221

Offset

1,2

Comments

Row 2 of A220738.

Links

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

Formula

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

Empirical g.f.: x*(1 - x^2 - x^3 - 2*x^4 + x^5) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + x + x^2)). - Colin Barker, Aug 03 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):
.69.47.00...00.69.47...00.67.47...69.49.00...00.00.00
.36.14.00...00.36.14...36.34.00...00.16.14...00.00.00

Crossrefs

Cf. A220738.

Sequence in context: A110320 A219230 A108890 * A337282 A366117 A027929

Adjacent sequences: A220736 A220737 A220738 * A220740 A220741 A220742

Keyword

nonn

Author

R. H. Hardin, Dec 18 2012

Status

approved