A262395 - OEIS

A262395

Difference between the numbers of trees on n vertices with an even number and an odd number of leaves.

1, 1, 0, 1, 0, 1, 1, 3, 2, 5, 5, 13, 13, 29, 32, 71, 81, 177, 209, 449, 538, 1148, 1415, 3002, 3736, 7862, 9930, 20877, 26648, 55756, 71767, 149860, 194507, 405332, 529708, 1101502, 1447956, 3006750, 3974959, 8242691, 10948355, 22673357, 30249668, 62583402, 83831176, 173259448, 232917913, 480970826, 648753720

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,8

COMMENTS

The sequence could be prepended with a(0)=1 and a(1)=-1. However, it is conjectured that for all n>=2, we have a(n)>=0 (cf. MathOverflow link).

LINKS

Table of n, a(n) for n=2..50.

MathOverflow, Counting trees according to endpoints, 2015.

FORMULA

a(n) = A262430(n) - A262431(n).

G.f.: x + A(x,-1), where A(x,y) is g.f. for A055290.

CROSSREFS