|
|
A008734
|
|
Molien series for 3-dimensional group [2+,n ] = 2*(n/2).
|
|
1
|
|
|
1, 0, 2, 0, 3, 1, 4, 2, 6, 3, 8, 4, 10, 6, 12, 8, 15, 10, 18, 12, 21, 15, 24, 18, 28, 21, 32, 24, 36, 28, 40, 32, 45, 36, 50, 40, 55, 45, 60, 50, 66, 55, 72, 60, 78, 66, 84, 72, 91, 78, 98, 84, 105, 91, 112, 98, 120
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,0,1,-1,-1,1).
|
|
FORMULA
|
G.f.: (1 -x +x^2 -x^3 +x^4)/((1+x^2)*(1+x^4)*(1+x)^2*(1-x)^3). - R. J. Mathar, Dec 18 2014
|
|
MAPLE
|
seq(coeff(series((1+x^5)/((1-x^2)^2*(1-x^8)), x, n+1), x, n), n = 0 .. 70); # modified by G. C. Greubel, Jul 30 2019
|
|
MATHEMATICA
|
CoefficientList[Series[(1+x^5)/((1-x^2)^2*(1-x^8)), {x, 0, 70}], x] (* G. C. Greubel, Jul 30 2019 *)
|
|
PROG
|
(PARI) my(x='x+O('x^70)); Vec((1+x^5)/((1-x^2)^2*(1-x^8))) \\ G. C. Greubel, Jul 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^5)/((1-x^2)^2*(1-x^8)) )); // G. C. Greubel, Jul 30 2019
(Sage) ((1+x^5)/((1-x^2)^2*(1-x^8))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019
(GAP) a:=[1, 0, 2, 0, 3, 1, 4, 2, 6, 3, 8];; for n in [12..70] do a[n]:=a[n-1]+a[n-2]-a[n-3] +a[n-8]-a[n-9]-a[n-10]+a[n-11]; od; a; # G. C. Greubel, Jul 30 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|