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

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...

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.6.3, p. 304.

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

Cf. A000055, A000081, A005200, A005201.

Sequence in context: A019902 A021147 A246709 * A330564 A195296 A396743

Adjacent sequences: A051493 A051494 A051495 * A051497 A051498 A051499

Keyword

nonn,cons

Author

David Broadhurst

Status

approved