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A008725 Molien series for 3-dimensional group [2,n] = *22n. 5
1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 19, 21, 24, 27, 30, 33, 36, 39, 42, 46, 50, 54, 58, 62, 66, 70, 75, 80, 85, 90, 95, 100, 105, 111, 117, 123, 129, 135, 141, 147, 154, 161, 168, 175, 182, 189, 196, 204, 212, 220, 228, 236, 244, 252, 261, 270, 279, 288, 297, 306 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 190

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,-2,1).

FORMULA

G.f.: 1/(1-x)^2/(1-x^7).

a(n) = sum(floor(j/7), {j,0,n+7}), a(n-7) = (1/2)floor(n/7)*(2n-5 -7*floor(n/7)). - Mitch Harris, Sep 08 2008

a(n) = +2*a(n-1) -a(n-2) +a(n-7) -2*a(n-8) +a(n-9). - R. J. Mathar, Apr 20 2010

MAPLE

1/(1-x)^2/(1-x^7): seq(coeff(series(%, x, n+1), x, n), n=0..80);

MATHEMATICA

s=0; lst={}; Do[AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 14 2010 *)

CoefficientList[Series[1 / (1 - x)^2 / (1 - x^7), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 11 2013 *)

LinearRecurrence[{2, -1, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 7, 9, 11}, 70] (* Harvey P. Dale, Sep 27 2014 *)

CROSSREFS

Sequence in context: A281613 A174738 A011867 * A275673 A026445 A279078

Adjacent sequences:  A008722 A008723 A008724 * A008726 A008727 A008728

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Mar 14 2010

STATUS

approved

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Last modified March 24 20:06 EDT 2017. Contains 283993 sequences.