A077014 Number of ways that a directed line (or river) that starts in the south can cross an east-west road n times.

2, 1, 2, 2, 6, 8, 28, 42, 162, 262, 1076, 1828, 7852, 13820, 61388, 110954, 505878, 933458, 4345660, 8152860, 38608380, 73424650, 352686780, 678390116, 3298016912, 6405031050, 31461151108, 61606881612, 305327366988, 602188541928, 3007925909860, 5969806669034

Offset

0,1

Comments

The difference between this and A005316 is that here the river can also end up in the southwest. In A005316 it was required to end up in the northeast or southeast.

Or, number of ways that an undirected line that starts and ends anywhere can cross an east-west road n times.

Links

Table of n, a(n) for n=0..31.

S. Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025 [math.CO], 2013.

S. Legendre, Foldings and Meanders, Australasian Journal of Combinatorics 58(2) (2014), 275-291.

Formula

Equals A005316(n) if n odd, or 2*A005316(n) if n even (because then each solution to A005316 can be reflected in a vertical mirror to give another solution).

Mathematica

A005316 = Cases[Import["https://oeis.org/A005316/b005316.txt", "Table"], {_, _}][[All, 2]];
a[n_] := If[OddQ[n], A005316[[n+1]], 2*A005316[[n+1]] ];
a /@ Range[0, 31] (* Jean-François Alcover, Sep 07 2019 *)

Crossrefs

Sequence in context: A334500 A081727 A000020 * A093655 A023140 A145859

Adjacent sequences: A077011 A077012 A077013 * A077015 A077016 A077017

Keyword

nonn

Author

N. J. A. Sloane and Jon Wild, Nov 29 2002

Status

approved