OFFSET
0,3
COMMENTS
a(n) are also coefficients in a Molien Series for G = H x T x O, where H is Hermitian conjugacy, T is Time-reversal, and O is Octahedral. |G| = 96.
Harter et al. give some terms. Compare first four values of a(n) with Eq. 8 of Dhont, Sadovskií, Zhilinskií, and Boudon (see links).
LINKS
Guillaume Dhont, D. A. Sadovskií, B. I. Zhilinskií, & Vincent Boudon, Analysis of the "unusual" vibrational components of triply degenerate vibrational mode v6 of Mo(CO)6 based on the classical interpretation of the effective rotation-vibration Hamiltonian, J. Mol. Spectrosc. 201, 95-108 (2000) (alternate copy).
W. G. Harter, H. W. Galbraith, and C. W. Patterson, Centrifugal and Coriolis effects on level cluster patterns for T(v3) rovibrational bands in spherical top molecules, J. Chem. Phys, 69, 4896 (1978).
N. J. A. Sloane, Error-correcting codes and invariant theory: new applications of a nineteenth-century technique, American Mathematical Monthly (1977): 82-107.
Richard P. Stanley, Invariants of finite groups and their applications to combinatorics, Bulletin of the American Mathematical Society 1.3 (1979): 475-511.
Index entries for linear recurrences with constant coefficients, signature (0, 2, 0, 0, 0, -2, 0, 1).
FORMULA
MATHEMATICA
(D[(1 + x + x^2)/((1 - x^2)^3 (1 + x^2)), {x, #}]/#! /. x -> 0) & /@
Range[0, 20]
CoefficientList[Series[(1 + x + x^2)/((1 - x^2)^3 (1 + x^2)), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 22 2015 *)
LinearRecurrence[{0, 2, 0, 0, 0, -2, 0, 1}, {1, 1, 3, 2, 6, 4, 10, 6}, 60] (* Robert G. Wilson v, Jul 22 2015 *)
PROG
(PARI) Vec((1 + x + x^2)/((1 - x^2)^3*(1 + x^2)) + O(x^80)) \\ Michel Marcus, Jul 20 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Bradley Klee, Jul 19 2015
EXTENSIONS
More terms from Michel Marcus, Jul 20 2015
STATUS
approved