A220559 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly one horizontal or antidiagonal neighbor.

8, 149, 2604, 45966, 810778, 14298089, 252139015, 4446314533, 78407942556, 1382674335890, 24382584703194, 429971411669361, 7582273047532603, 133708574584054949, 2357865880743076540, 41579468847568886038

Offset

1,1

Comments

Column 5 of A220562.

Links

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

Formula

Empirical: a(n) = 21*a(n-1) - 62*a(n-2) + 47*a(n-3) - 5*a(n-4) for n>5.

Empirical g.f.: x*(8 - 19*x - 29*x^2 + 144*x^3 - 23*x^4) / ((1 - x)*(1 - 20*x + 42*x^2 - 5*x^3)). - Colin Barker, Jul 31 2018

Example

Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
..0..0..0..6..4....0..0..0..6..4....0..0..0..6..4....0..0..6..4..0
..6..4..0..6..4....0..6..4..0..0....0..6..4..7..0....0..7..7..7..0
..0..6..4..0..0....0..6..4..0..0....0..0..3..0..0....3..3..3..0..0

Crossrefs

Cf. A220562.

Sequence in context: A244028 A075351 A302063 * A264642 A300872 A217502

Adjacent sequences: A220556 A220557 A220558 * A220560 A220561 A220562

Keyword

nonn

Author

R. H. Hardin, Dec 16 2012

Status

approved