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

0,3

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A256338 A256331 A292875 * A355291 A325219 A205580

Adjacent sequences: A077051 A077052 A077053 * A077055 A077056 A077057

Keyword

nonn

Author

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

Status

approved