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A165515 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I. 1
1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388395, 435214379250840, 12621216997908960, 366015292928763240, 10614443494626832560, 307818861335266403640, 8926746978464285228160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170749, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..682

Index entries for linear recurrences with constant coefficients, signature (28,28,28,28,28,28,28,28,-406).

FORMULA

G.f.: (t^9 +2*t^8 +2*t^7 +2*t^6 +2*t^5 +2*t^4 +2*t^3 +2*t^2 +2*t +1)/( 406*t^9 -28*t^8 -28*t^7 -28*t^6 -28*t^5 -28*t^4 -28*t^3 -28*t^2 -28*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 16 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), {t, 0, 20}], t] (* G. C. Greubel, Oct 21 2018 *)

coxG[{9, 406, -28}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 16 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10)) \\ G. C. Greubel, Oct 21 2018

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10) )); // G. C. Greubel, Oct 21 2018

(Sage)

def A165515_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10)).list()

A165515_list(20) # G. C. Greubel, Sep 16 2019

(GAP) a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388395];; for n in [10..20] do a[n]:=28*Sum([1..8], j-> a[n-j]) -406*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

CROSSREFS

Sequence in context: A164027 A164666 A164983 * A166026 A166424 A166617

Adjacent sequences:  A165512 A165513 A165514 * A165516 A165517 A165518

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 03 2009

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)