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A260253
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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).
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1
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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
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OFFSET
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0,3
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COMMENTS
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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).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1,0,1,0,-2,0,1).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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