A038381 Number of perifusenes with one internal vertex and symmetry point group C_s.

0, 0, 0, 0, 1, 4, 23, 103, 477, 2132, 9647, 43549, 197757, 901162, 4125636, 18962997, 87508095, 405285316, 1883445191, 8780327545, 41052409755, 192461538607, 904573028990, 4261485478861, 20119936933822, 95186854957397

Offset

0,6

References

S. J. Cyvin et al., Number of perifusenes with one internal vertex, Rev. Roumaine Chem., 38 (1993), 65-77.

Links

Table of n, a(n) for n=0..25.

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

Sequence in context: A197854 A317599 A122738 * A241777 A321614 A082970

Adjacent sequences: A038378 A038379 A038380 * A038382 A038383 A038384

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Emeric Deutsch, May 14 2004

Name clarified by Sean A. Irvine, Jan 13 2021

Status

approved