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

%I #18 Sep 27 2023 13:59:30

%S 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,

%T 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,

%U 4,5,0,5,0,1,7,0,7,4,7,3,8,9,6,7,5,6,5,4

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

%C It is the spectral radius of the paw graph.

%H Alberto Seeger and David Sossa, <a href="https://ajc.maths.uq.edu.au/pdf/87/ajc_v87_p258.pdf">Infinite families of connected graphs with equal spectral radius</a>, Australas. J. Combin. 87 (2) (2023), 258-276. See p. 260.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PawGraph.html">Paw Graph</a>

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

%e 2.1700864866260337227032557644253...

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

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

%K nonn,cons

%O 1,1

%A _Stefano Spezia_, Sep 19 2023