A260220 Number of symmetry-allowed, linearly-independent terms at n-th order in the expansion of T1 x t1 rovibrational perturbation matrix H(Jx,Jy,Jz).
1, 1, 3, 2, 6, 4, 10, 6, 15, 9, 21, 12, 28, 16, 36, 20, 45, 25, 55, 30, 66, 36, 78, 42, 91, 49, 105, 56, 120, 64, 136, 72, 153, 81, 171, 90, 190, 100, 210, 110, 231, 121, 253, 132, 276, 144, 300, 156, 325, 169, 351, 182, 378, 196, 406, 210, 435, 225, 465, 240
Offset: 0
Keywords
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 Molien series
- Index entries for linear recurrences with constant coefficients, signature (0, 2, 0, 0, 0, -2, 0, 1).
Programs
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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 *) -
PARI
Vec((1 + x + x^2)/((1 - x^2)^3*(1 + x^2)) + O(x^80)) \\ Michel Marcus, Jul 20 2015
Formula
Extensions
More terms from Michel Marcus, Jul 20 2015
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