OFFSET
0,6
REFERENCES
S. J. Cyvin et al., Number of perifusenes with one internal vertex, Rev. Roumaine Chem., 38 (1993), 65-77.
LINKS
S. J. Cyvin, F. Zhang and J. Brunvoll, Enumeration of perifusenes with one internal vertex: A complete mathematical solution, J. Math. Chem., 11 (1992), 283-292.
FORMULA
G.f.: (1-11x+21x^2-9x^3)/2-(4-18x+17x^2)*(1-x)^(1/2)*(1-5x)^(1/2)/6+x(1-x^2)^(1/2)*(1-5x^2)^(1/2)/2+(1-x^3)^(1/2)*(1-5x^3)^(1/2)/6. - Emeric Deutsch, May 14 2004
a(n) ~ 9 * 5^(n - 5/2) / (2 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Jan 14 2021
MATHEMATICA
CoefficientList[Series[(1 - 11*x + 21*x^2 - 9*x^3)/2 - Sqrt[1 - 5*x]*Sqrt[1 - x]*(4 - 18*x + 17*x^2)/6 + x*Sqrt[1 - 5*x^2]*Sqrt[1 - x^2]/2 + Sqrt[1 - 5*x^3] * Sqrt[1 - x^3]/6, {x, 0, 30}], x] (* Vaclav Kotesovec, Jan 14 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, May 14 2004
Name clarified by Sean A. Irvine, Jan 13 2021
STATUS
approved