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Number of trees with n unlabeled nodes such that all nodes with degree >2 lie on a single path with length equal to the tree's diameter.
2

%I #13 Dec 12 2016 09:36:43

%S 1,1,1,1,2,3,6,11,23,47,103,223,503,1132,2602,5986,13922,32433,75994,

%T 178354,419945,990134,2339033,5531459

%N Number of trees with n unlabeled nodes such that all nodes with degree >2 lie on a single path with length equal to the tree's diameter.

%C First differs from A000055 at a(10).

%C First differs from A130131 at a(10), n >= 1.

%C The ratio of consecutive terms seems to tend to some limit. - _Andrey Zabolotskiy_, Dec 12 2016

%H Andrey Zabolotskiy, <a href="/A277795/a277795.py.txt">Python script for the sequence</a>

%e From _Andrey Zabolotskiy_, Nov 21 2016: (Start)

%e Three trees that are counted in A000055(10) but not in a(10):

%e (1)

%e o o-o-o

%e | |

%e o----o

%e | |

%e o o-o-o

%e (2)

%e o-o-o

%e |

%e o-o-o-o

%e |

%e o-o-o

%e (3)

%e o-o-o-o-o-o-o

%e |

%e o-o-o

%e (End)

%Y Cf. A000055, A130131.

%K nonn,more

%O 0,5

%A _Gabriel Burns_, Oct 31 2016

%E Corrections and more terms from _Andrey Zabolotskiy_, Nov 21 2016