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A165786 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828828, 2259801600, 15818609856, 110730259584, 775111751232, 5425781797632, 37980469356480, 265863262906752, 1861042682227008, 13027297668747264 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003950, 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..500

Index entries for linear recurrences with constant coefficients, signature (6,6,6,6,6,6,6,6,6,-21).

FORMULA

G.f.: (t^10 + 2*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)/(21*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 22 2019

MATHEMATICA

With[{num=Total[2t^Range[9]]+t^10+1, den=Total[-6 t^Range[9]]+21t^10+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 20 2011 *)

CoefficientList[Series[(1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11), {t, 0, 20}], t] (* or *) coxG[{10, 21, -6}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 22 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11)) \\ G. C. Greubel, Sep 22 2019

(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11) )); // G. C. Greubel, Sep 22 2019

(Sage)

def A165786_list(prec):

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

return P( (1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11) ).list()

A165786_list(30) # G. C. Greubel, Sep 22 2019

(GAP) a:=[8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828828];; for n in [11..20] do a[n]:=6*Sum([1..9], j-> a[n-j]) -21*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019

CROSSREFS

Sequence in context: A164373 A164769 A165215 * A166366 A166538 A166910

Adjacent sequences: A165783 A165784 A165785 * A165787 A165788 A165789

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified December 8 01:00 EST 2022. Contains 358671 sequences. (Running on oeis4.)