|
|
A277493
|
|
Number of planar rooted Eulerian orientations (i.e., planar directed Eulerian maps with in-degree and out-degree equal for each vertex) with n edges.
|
|
4
|
|
|
1, 2, 10, 66, 504, 4216, 37548, 350090, 3380520, 33558024, 340670720, 3522993656, 37003723200, 393856445664, 4240313009272, 46109094112170
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(n) is the coefficient of t^n in the generating function O(t) = sum_w O_w(t), where w is any binary word on the alphabet {0,1} having as many 0's as 1's.
The series O_w(t) are defined by O_epsilon(t) = 1 (for the empty word epsilon) and O_w(t) = t* sum_{w=aubv} O_u(t)*O_v(t) + t* sum_u O_uw'(t), where: a is a binary letter (0 or 1), b = 1-a, w' is the suffix of w of length |w|-1.
|
|
LINKS
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|