A220590 Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly two king-move neighbors.

1, 8, 33, 155, 710, 3265, 15009, 68992, 317149, 1457879, 6701646, 30806405, 141612197, 650968960, 2992401777, 13755599635, 63232324870, 290669037689, 1336159782873, 6142116062912, 28234340094485, 129788814214207

Offset

1,2

Comments

Column 2 of A220595.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 7*a(n-2) + 2*a(n-3) - 2*a(n-4).

Empirical g.f.: x*(1 + x)*(1 + 4*x - 2*x^2) / (1 - 3*x - 7*x^2 - 2*x^3 + 2*x^4). - Colin Barker, Aug 01 2018

Example

Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10):
.69.47...00.00...00.00...00.00...69.47...68.48...89.00...69.48...00.00...68.48
.39.17...69.48...00.78...68.48...39.18...29.27...29.17...00.12...69.47...28.28
.36.14...00.12...36.24...26.24...00.12...36.14...36.14...00.00...36.14...26.24

Crossrefs

Cf. A220595.

Sequence in context: A349101 A297683 A346819 * A001407 A005398 A240044

Adjacent sequences: A220587 A220588 A220589 * A220591 A220592 A220593

Keyword

nonn

Author

R. H. Hardin, Dec 16 2012

Status

approved