login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A260253 Number of symmetry-allowed, linearly-independent terms at n-th order in the expansion of E x (e+a) rovibrational perturbation matrix H(Jx,Jy,Jz). 1
1, 0, 4, 1, 9, 2, 16, 4, 25, 7, 36, 10, 49, 14, 64, 19, 81, 24, 100, 30, 121, 37, 144, 44, 169, 52, 196, 61, 225, 70, 256, 80, 289, 91, 324, 102, 361, 114, 400, 127, 441, 140, 484, 154, 529, 169, 576, 184, 625, 200, 676, 217, 729, 234, 784, 252, 841, 271 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) are also coefficients in a Molien Series for G = H x T x D3, where H is Hermitian conjugacy, T is Time-reversal, and D3 is triangular Dihedral. |G| = 24.

Harter et al. give only one second-order term, while Sadovskií et al. give only two (see links).

LINKS

Table of n, a(n) for n=0..57.

W. G. Harter, H. W. Galbraith, and C. W. Patterson, Energy level cluster analysis for E(v2) vibration rotation spectrum of spherical top molecules, J. Chem. Phys, 69, 4888 (1978).

D. A. Sadovskií and B. I. Zhilinskií, Qualitative analysis of vibration-rotation Hamiltonians for spherical top molecules, Molecular Physics 65, 1 (1988).

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 Molien series

FORMULA

G.f.: (1 + 2 * x^2 + x^3 + 2 * x^4 + x^6 + x^7)/((1 - x^2)^3 *(1 + x^2 + x^4)).

MATHEMATICA

D[(1 + 2 x^2 + x^3 + 2 x^4 + x^6 + x^7)/((1 - x^2)^3*(1 + x^2 + x^4)), {x, #}]/#!/.x -> 0 & /@ Range[0, 30]

CoefficientList[Series[(1 + 2 x^2 + x^3 + 2 x^4 + x^6 + x^7)/((1 - x^2)^3 (1 + x^2 + x^4)), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 22 2015 *)

PROG

(PARI) Vec((1 + 2 * x^2 + x^3 + 2 * x^4 + x^6 + x^7)/((1 - x^2)^3 *(1 + x^2 + x^4)) + O(x^90)) \\ Michel Marcus, Aug 05 2015

CROSSREFS

Cf. A007980, A002264, A260220.

Sequence in context: A306744 A304526 A333352 * A261981 A153265 A331153

Adjacent sequences:  A260250 A260251 A260252 * A260254 A260255 A260256

KEYWORD

nonn

AUTHOR

Bradley Klee, Jul 20 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)