A365814 Decimal expansion of the largest root of the polynomial x^3 - 2*x^2 - 2*x + 2.

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

Offset: 1

Author

Stefano Spezia, Sep 19 2023

Keywords

• nonn
• cons

Comments

It is the spectral radius of the house graph.

Examples

			2.4811943040920156226335372412168571805527452...
		

Links

• Alberto Seeger and David Sossa, Infinite families of connected graphs with equal spectral radius, Australas. J. Combin. 87 (2) (2023), 258-276. See p. 270.
• Eric Weisstein's World of Mathematics, House Graph

Crossrefs

Cf. A078564, A209927, A222132, A365750.

Programs

Maple

Digits:= 140:
fsolve(x^3-2*x^2-2*x+2)[3];  # Alois P. Heinz, Sep 19 2023

Mathematica

First[RealDigits[Root[#^3-2#^2-2#+2,3,0],10,88]]

Formula

Equals (2 + 10/(3*i*sqrt(111) - 1)^(1/3) + (3*i*sqrt(111) - 1)^(1/3))/3, where i denotes the imaginary unit.