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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, 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
0,3
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
FORMULA
G.f.: (1 + x + x^2)/((1 - x^2)^3*(1 + x^2)).
a( 4 n+1 ) = A000290(n+1);
a( 4 n+3 ) = 2*A000217(n+1);
a( 2 n ) = A000217(n+1).
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
Sequence in context: A105354 A094077 A375113 * A249742 A246276 A091018
KEYWORD
nonn
AUTHOR
Bradley Klee, Jul 19 2015
EXTENSIONS
More terms from Michel Marcus, Jul 20 2015
STATUS
approved