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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
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.
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)).
a(n)= 2*a(n-2) -a(n-4) +a(n-6) -2*a(n-8) +a(n-10). - R. J. Mathar, Jul 20 2023
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 (bisection), A002264, A260220, A000290 (bisection).
Sequence in context: A306744 A304526 A333352 * A261981 A153265 A331153
KEYWORD
nonn,easy
AUTHOR
Bradley Klee, Jul 20 2015
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)