OFFSET
0,31
COMMENTS
Meyer's generating function h(t,G) generates the sequence of the dimensions of the spaces of G-invariant harmonic polynomials of each degree, where G is a point group on three-dimensional Euclidean space. For G=I, the icosahedral rotation group, the generating function gives rise to this sequence. See Table 1, p. 143.
LINKS
Burnett Meyer, On the symmetries of spherical harmonics, Canadian Journal of Mathematics 6 (1954): 135-157.
FORMULA
G.f.: (1 + t^15) / ( (1 - t^10) * (1 - t^6) ).
a(n) = -a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6) - a(n-8) - a(n-9) for n>8. - Colin Barker, May 04 2019
MATHEMATICA
CoefficientList[ Series[(1 - t^10)^(-1) (1 - t^6)^(-1) (1 + t^15), {t, 0, 100}], t]
PROG
(PARI) Vec((1 + x - x^3 - x^4 - x^5 + x^7 + x^8) / ((1 - x)^2*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, May 04 2019
CROSSREFS
KEYWORD
dead
AUTHOR
William Lionheart, May 04 2019
STATUS
approved