A272354 Decimal expansion of 'kappa', an asymptotic enumeration constant related to unit interval graphs.

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, 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, 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

Offset

0,1

References

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

Links

Table of n, a(n) for n=0..98.

Formula

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)).

Example

0.6231198963919113852048660293282228516818111157691828509147523335...

Mathematica

digits = 99; psi[x_] := (1 + 2*x - Sqrt[1 - 4*x]*Sqrt[1 - 4*x^2])/(4*Sqrt[1 - 4*x^2]);
kappa = Exp[-Sqrt[3]/4]*Exp[-NSum[psi[4^(-j)]/j, {j, 2, Infinity}, NSumTerms -> 200, WorkingPrecision -> digits + 5]]; RealDigits[kappa, 10, digits][[1]]

Crossrefs

Sequence in context: A065280 A247672 A188726 * A353121 A196552 A062614

Adjacent sequences: A272351 A272352 A272353 * A272355 A272356 A272357

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 30 2016

Status

approved