A363682 Number of plane bipolar posets (i.e., plane bipolar orientations with no transitive edge) with n edges.

1, 1, 1, 2, 5, 12, 32, 93, 279, 872, 2830, 9433, 32223, 112527, 400370, 1448520, 5320023, 19802827, 74612164, 284238390, 1093757436, 4247742956, 16636921148, 65671960544, 261111950308, 1045172796381, 4209807155949, 17055625810984, 69476952146529, 284467866640048

Offset: 1

Author

Éric Fusy, Jun 16 2023

Keywords

• nonn

Comments

a(n) is also the number of walks of length n-1 in the quadrant, starting and ending at the origin, with step-set {0,E,S,NW,SE} (where 0 is the stay-step).

Links

• Éric Fusy, Erkan Narmanli, and Gilles Schaeffer, On the enumeration of plane bipolar posets and transversal structures, arXiv:2105.06955 [math.CO], 2021-2022.

Crossrefs

Cf. A001181, A296419, A117106, A151335.

Programs

Maple

A:=proc(n,i,j) option remember:
if n=0 and i=0 and j=0 then return 1:
elif n<=0 or j<0 or i<0 then return 0:
else
return A(n-1,i,j)+A(n-1,i-1,j)+A(n-1,i,j+1)+A(n-1,i+1,j-1)+A(n-1,i-1,j+1):
fi:
end proc:
seq(A(n-1,0,0),n=1..20);