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A008725 Molien series for 3-dimensional group [2,n] = *22n. 6
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

COMMENTS

a(n) is the number of partitions of n into parts 1 and 7, where there are two kinds of part 1. - Joerg Arndt, Sep 27 2020

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)).

From Mitch Harris, Sep 08 2008: (Start)

a(n) = Sum_{j=0..n+7} floor(j/7).

a(n-7) = (1/2)*floor(n/7)*(2*n - 5 - 7*floor(n/7)). (End)

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

a(n) = A011867(n+5). - Pontus von Brömssen, Sep 27 2020

MAPLE

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

MATHEMATICA

CoefficientList[Series[1/((1-x)^2*(1-x^7)), {x, 0, 80}], 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}, 80] (* Harvey P. Dale, Sep 27 2014 *)

PROG

(PARI) my(x='x+O('x^80)); Vec(1/((1-x)^2*(1-x^7))) \\ G. C. Greubel, Sep 09 2019

(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x)^2*(1-x^7)) )); // G. C. Greubel, Sep 09 2019

(Sage)

def A008725_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P(1/((1-x)^2*(1-x^7))).list()

A008725_list(80) # G. C. Greubel, Sep 09 2019

(GAP) a:=[1, 2, 3, 4, 5, 6, 7, 9, 11];; for n in [10..80] do a[n]:=2*a[n-1] -a[n-2]+a[n-7]-2*a[n-8]+a[n-9]; od; a; # G. C. Greubel, Sep 09 2019

CROSSREFS

Cf. A011867.

Sequence in context: A281613 A174738 A011867 * A275673 A347327 A026445

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 December 9 02:22 EST 2022. Contains 358698 sequences. (Running on oeis4.)