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

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

Cf. A055290, A055277.

Sequence in context: A182714 A343342 A338470 * A198755 A134237 A341521

Adjacent sequences: A262392 A262393 A262394 * A262396 A262397 A262398

Keyword

nonn

Author

Max Alekseyev, Sep 21 2015

Status

approved