login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005916 Molien series for a certain group of order 52. 1
1, 0, 1, 0, 2, 1, 3, 2, 5, 4, 7, 7, 11, 11, 15, 16, 21, 22, 28, 30, 37, 39, 47, 50, 60, 63, 74, 78, 91, 95, 109, 115, 131, 137, 154, 162, 181, 190, 210, 221, 243, 255, 278, 292, 318, 333, 360, 377, 407, 425, 457, 477, 512, 533, 570, 593, 633, 658, 700, 727 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The group is a semidirect product C13: C4 presented by <g, h | g^13=1, h^4=1, hg = g^5 h>. The group has 3 irreducible characters of degree 4, all of which have the same Molien series, this sequence. - Eric M. Schmidt, Feb 02 2013

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1).

FORMULA

G.f.: (1-x+x^5+x^11-x^13+x^14)/((1-x)*(1-x^2)*(1-x^4)*(1-x^13)). - Colin Barker, Jan 31 2013, confirmed and simplified by Eric M. Schmidt, Feb 02 2013

a(n) ~ (1/312)*n^3. - Ralf Stephan, Apr 29 2014

MAPLE

m:=60; S:=series((1-x+x^5+x^11-x^13+x^14)/((1-x)*(1-x^2)*(1-x^4)*(1-x^13)), x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Feb 06 2020

MATHEMATICA

CoefficientList[Series[(1-x+x^5+x^11-x^13+x^14)/((1-x)*(1-x^2)*(1-x^4)*(1-x^13)), {x, 0, 60}], x] (* G. C. Greubel, Feb 06 2020 *)

PROG

(GAP) series:=MolienSeries(First(Irr(SmallGroup(52, 3)), irr->Degree(irr)=4));; List([0..30], i->ValueMolienSeries(series, i)); # Eric M. Schmidt, Feb 02 2013

(PARI) Vec( (1-x+x^5+x^11-x^13+x^14)/((1-x)*(1-x^2)*(1-x^4)*(1-x^13)) +O('x^60) ) \\ G. C. Greubel, Feb 06 2020

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x+x^5+x^11-x^13+x^14)/((1-x)*(1-x^2)*(1-x^4)*(1-x^13)) )); // G. C. Greubel, Feb 06 2020

(Sage)

def A005916_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( (1-x+x^5+x^11-x^13+x^14)/((1-x)*(1-x^2)*(1-x^4)*(1-x^13)) ).list()

A005916_list(60) # G. C. Greubel, Feb 06 2020

CROSSREFS

Sequence in context: A238782 A058736 A097451 * A034392 A181531 A034393

Adjacent sequences:  A005913 A005914 A005915 * A005917 A005918 A005919

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Eric M. Schmidt, Feb 02 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 10 15:47 EDT 2021. Contains 342845 sequences. (Running on oeis4.)