OFFSET
0,5
REFERENCES
J. H. Conway and N. J. A. Sloane, computed circa 1977.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canadian J. Math. 6, (1954). 274--304. MR0059914 (15,600b).
Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,1,-1,-1,0,-1,0,1).
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
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved