A077054 Number of ways a river can cross a road 2n times.

1, 1, 3, 14, 81, 538, 3926, 30694, 252939, 2172830, 19304190, 176343390, 1649008456, 15730575554, 152663683494, 1503962954930, 15012865733351, 151622652413194, 1547365078534578, 15939972379349178, 165597452660771610, 1733609081727968492

Offset: 0

Author

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

Keywords

• nonn

Comments

More precisely, number of ways that a river (or directed line) that starts in the southwest and flows east can cross an east-west road 2n times (bisection of A005316).

Also number of ways a loop can cross two parallel roads 2n times. Some portion of loop must lie below lower road.

Links

• Jean-François Alcover, Table of n, a(n) for n = 0..27

Crossrefs

Bisection of A005316. Cf. A005315, A085873, A086031.

Programs

Mathematica

A005316 = Cases[Import["https://oeis.org/A005316/b005316.txt", "Table"], {, }][[All, 2]];
a[n_] := A005316[[2n+1]];
a /@ Range[0, 27] (* Jean-François Alcover, Sep 20 2019 *)

Formula

a(n) = A005316(2*n).