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A051496 Decimal expansion of probability that a point of an infinite (rooted) tree is fixed by every automorphism of the tree. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

F. Harary and E. M. Palmer derive certain functional equations and, using the methods of G. Polya (Acta Math. 68 (1937), 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 ...

REFERENCES

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

LINKS

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

D. J. Broadhurst and D. Kreimer, Rooted-tree paper

Index entries for sequences related to trees

Index entries for sequences related to rooted trees

EXAMPLE

0.6995388700609892332166312186...

CROSSREFS

Equals \lim_{n\to\infty} A005200[n]/(n*A000081[n]) = \lim_{n\to\infty} A005201[n]/(n*A000055[n])

Sequence in context: A019902 A021147 A246709 * A195296 A273951 A100403

Adjacent sequences:  A051493 A051494 A051495 * A051497 A051498 A051499

KEYWORD

nonn,cons

AUTHOR

David Broadhurst

STATUS

approved

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Last modified November 18 07:01 EST 2018. Contains 317279 sequences. (Running on oeis4.)