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A276813
Continued fraction for the ratio of the lowest two Dirichlet eigenvalues of the Laplacian within the regular pentagon.
1
2, 1, 1, 8, 1, 4, 2, 2, 16, 3, 3, 1, 3, 1, 1, 2, 1, 1, 3, 1, 3, 3, 5, 1, 13, 1, 4, 1, 1, 13, 4, 3, 1, 4, 1, 1, 6, 5, 9, 1, 13, 2, 15, 1, 2, 3, 3, 1, 4, 9, 2, 14, 1, 4, 1, 7, 1, 1, 11, 1, 4, 5, 2, 3, 2, 1, 14, 1, 1, 2, 1, 1, 1, 1, 20, 3, 2, 1, 2, 2, 7, 1, 2
OFFSET
1,1
COMMENTS
The eigenvalues of the Laplacian within the regular pentagon with Dirichlet boundary conditions are calculated to at least 1000 digits. The ratio of the second eigenvalue to the first is calculated and expressed as a continued fraction. The ratio has an advantage since it is independent of the pentagon area. All terms in this expansion are correct.
LINKS
Robert Stephen Jones, Table of n, a(n) for n = 1..978
EXAMPLE
2.52683872... = 2+1/(1+1/(1+1/(8+1/(1+...)))).
CROSSREFS
Cf. A262823.
Sequence in context: A060865 A078689 A230069 * A134470 A342992 A119418
KEYWORD
nonn,cofr
AUTHOR
STATUS
approved