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A005868
Molien series for 3-dimensional representation of Z2 X (double cover of A6), u.g.g.r. # 27 of Shephard and Todd.
1
1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 1, 7, 1, 8, 2, 10, 2, 11, 3, 13, 4, 14, 5, 16, 6, 18, 7, 20, 8, 22, 10, 24, 11, 26, 13, 29, 14, 31, 16, 34, 18, 36, 20, 39, 22, 42, 24, 45, 26, 48, 29, 51, 31, 54, 34, 58, 36, 61, 39, 65, 42, 68, 45, 72, 48, 76, 51
OFFSET
0,5
REFERENCES
J. H. Conway and N. J. A. Sloane, computed circa 1977.
LINKS
G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canadian J. Math. 6, (1954). 274--304. MR0059914 (15,600b).
FORMULA
G.f.: (1-x+x^2)*(1+x-x^3-x^4-x^5+x^7+x^8)/((1-x)^3*(1+x)^2*(1+x^2)*(1+x+x^2+x^3+x^4)). - Colin Barker, Jan 08 2014
a(n) ~ 1/80*n^2. - Ralf Stephan, Apr 29 2014
a(n) = a(n-2)+a(n-4)+a(n-5)-a(n-6)-a(n-7)-a(n-9)+a(n-11). - Wesley Ivan Hurt, May 24 2021
MAPLE
(1+x^45)/(1-x^6)/(1-x^12)/(1-x^30):
seq(coeff(series(expand(%), x, 3*n+1), x, 3*n), n=0..100);
MATHEMATICA
CoefficientList[Series[(1-x+x^2)(1+x-x^3-x^4-x^5+x^7+x^8)/((1-x)^3 (1+x)^2 (1+x^2)(1+x+x^2+x^3+x^4), {x, 0, 70}], x]] (* Vincenzo Librandi, Apr 29 2014 *)
LinearRecurrence[{0, 1, 0, 1, 1, -1, -1, 0, -1, 0, 1}, {1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4}, 100] (* Harvey P. Dale, Aug 29 2016 *)
PROG
(PARI) Vec((x^10-x^5+1)/(-x^11+x^9+x^7+x^6-x^5-x^4-x^2+1) + O(x^100)) \\ Colin Barker, Jan 08 2014
(Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (1+x^15)/((1 - x^2)*(1-x^4)*(1-x^10)) )); // G. C. Greubel, Feb 06 2020
(Sage)
def A005868_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x^15)/((1-x^2)*(1-x^4)*(1-x^10)) ).list()
A005868_list(65) # G. C. Greubel, Feb 06 2020
CROSSREFS
Sequence in context: A008613 A165685 A035457 * A035455 A029191 A094098
KEYWORD
nonn,easy,nice
STATUS
approved