A365750 Decimal expansion of the largest root of the polynomial x^3 - x^2 - 3*x + 1.

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

Offset

1,1

Comments

It is the spectral radius of the paw graph.

Links

Table of n, a(n) for n=1..88.

Alberto Seeger and David Sossa, Infinite families of connected graphs with equal spectral radius, Australas. J. Combin. 87 (2) (2023), 258-276. See p. 260.

Eric Weisstein's World of Mathematics, Paw Graph

Formula

Equals 1/3 + (2/3)*sqrt(10)*cos((1/3)*arccos(10^(-3/2))).

Example

2.1700864866260337227032557644253...

Mathematica

First[RealDigits[1/3+2/3Sqrt[10]Cos[1/3ArcCos[10^(-3/2)]], 10, 88]]

Crossrefs

Cf. A010467, A209927, A222132, A352667, A365814.

Sequence in context: A320570 A300911 A347899 * A103114 A004561 A255984

Adjacent sequences: A365747 A365748 A365749 * A365751 A365752 A365753

Keyword

nonn,cons

Author

Stefano Spezia, Sep 19 2023

Status

approved