A272354 - OEIS

%I #19 Nov 17 2024 16:41:29

%S 6,2,3,1,1,9,8,9,6,3,9,1,9,1,1,3,8,5,2,0,4,8,6,6,0,2,9,3,2,8,2,2,2,8,

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

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

%N Decimal expansion of 'kappa', an asymptotic enumeration constant related to unit interval graphs.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6.7 More Graph Varieties, p. 309.

%F kappa = exp(-sqrt(3)/4)*exp(-Sum_{j >= 2} psi(4^(-j))/j), where psi(x)=(1 + 2*x - sqrt(1 - 4*x)*sqrt(1 - 4*x^2))/(4*sqrt(1 - 4*x^2)).

%e 0.6231198963919113852048660293282228516818111157691828509147523335...

%t digits = 99; psi[x_] := (1 + 2*x - Sqrt[1 - 4*x]*Sqrt[1 - 4*x^2])/(4*Sqrt[1 - 4*x^2]);

%t kappa = Exp[-Sqrt[3]/4]*Exp[-NSum[psi[4^(-j)]/j, {j, 2, Infinity}, NSumTerms -> 200, WorkingPrecision -> digits + 5]]; RealDigits[kappa, 10, digits][[1]]

%K nonn,cons,changed

%O 0,1

%A _Jean-François Alcover_, Apr 30 2016