A051496 - OEIS

A051496

Decimal expansion of the probability that a point of an infinite (rooted) tree is fixed by every automorphism of the tree.

6, 9, 9, 5, 3, 8, 8, 7, 0, 0, 6, 0, 9, 8, 9, 2, 3, 3, 2, 1, 6, 6, 3, 1, 2, 1, 8, 6, 2, 0, 1, 4, 2, 7, 6, 7, 1, 6, 3, 6, 8, 1, 4, 5, 5, 4, 6, 3, 5, 4, 2, 1, 6, 1, 9, 8, 9, 7, 5, 9, 2, 2, 0, 3, 2, 0, 0, 4, 6, 4, 1, 9, 2, 5, 6, 2, 9, 5, 6, 1, 2, 1, 4, 8, 7, 8, 4, 8, 0, 6, 0, 2, 8, 2, 6, 5, 4, 8

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OFFSET

0,1

COMMENTS

F. Harary and E. M. Palmer derive certain functional equations and, using the methods of G. Polya (Acta Math. (1937) Vol. 68, 145-254) and R. Otter (Ann. of Math. (2) 49 (1948), 583-599; Math. Rev. 10, 53), prove that the limiting probability of a fixed point in a large random tree, whether rooted or not, is 0.6995...

LINKS

Table of n, a(n) for n=0..97.

D. J. Broadhurst and D. Kreimer, Renormalization automated by Hopf algebra, arXiv:hep-th/9810087, 1998.

Frank Harary and Edgar M. Palmer, The probability that a point of a tree is fixed, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 3, 407-415.

Index entries for sequences related to trees

Index entries for sequences related to rooted trees

FORMULA

Equals lim_{n->oo} A005200(n)/(n*A000081(n)).

Equals lim_{n->oo} A005201(n)/(n*A000055(n)).

EXAMPLE

0.6995388700609892332166312186...

CROSSREFS