A085873 -id:A085873 - cp's OEIS frontend

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

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

nonn

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.

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

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

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 *)

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

A085874 a(1) = 2, a(n)= smallest prime of the form k*a(n-1) - 1 where k itself is a multiple of n.

Original entry on oeis.org

2, 3, 17, 67, 4019, 24113, 675163, 16203911, 2333363183, 23333631829, 7186758603331, 3880849645798739, 302706272372301641, 148326073462427804089, 4449782203872834122669, 498375606833757421738927

Offset: 1

Amarnath Murthy, Jul 07 2003

nonn

			a(2) = 3 = 2*2 - 1, a(3) = 17 = 6*3 -1, a(4) = 67 = 4*17 - 1, 2,6 and 4 are respectively multiples of 2,3 and 4.

Cf. A085873.

More terms from Ray Chandler, Jul 08 2003

cp's OEIS Frontend

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

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A085874 a(1) = 2, a(n)= smallest prime of the form k*a(n-1) - 1 where k itself is a multiple of n.

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