cp's OEIS Frontend

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

%I A077014 #23 Sep 08 2019 03:11:28
%S A077014 2,1,2,2,6,8,28,42,162,262,1076,1828,7852,13820,61388,110954,505878,
%T A077014 933458,4345660,8152860,38608380,73424650,352686780,678390116,
%U A077014 3298016912,6405031050,31461151108,61606881612,305327366988,602188541928,3007925909860,5969806669034
%N A077014 Number of ways that a directed line (or river) that starts in the south can cross an east-west road n times.
%C A077014 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.
%C A077014 Or, number of ways that an undirected line that starts and ends anywhere can cross an east-west road n times.
%H A077014 S. Legendre, <a href="http://arxiv.org/abs/1302.2025">Foldings and Meanders</a>, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
%H A077014 S. Legendre, <a href="http://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p275.pdf">Foldings and Meanders</a>, Australasian Journal of Combinatorics 58(2) (2014), 275-291.
%F A077014 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).
%t A077014 A005316 = Cases[Import["https://oeis.org/A005316/b005316.txt", "Table"], {_, _}][[All, 2]];
%t A077014 a[n_] := If[OddQ[n], A005316[[n+1]], 2*A005316[[n+1]] ];
%t A077014 a /@ Range[0, 31] (* _Jean-François Alcover_, Sep 07 2019 *)
%K A077014 nonn
%O A077014 0,1
%A A077014 _N. J. A. Sloane_ and _Jon Wild_, Nov 29 2002