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A166004 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648426, 8589706234144560, 240511774555729782, 6734329687551532752, 188561231251193685024, 5279714475026444683776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170748, 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 (27,27,27,27,27,27,27,27,27,-378).

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)/(378*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-28*t+405*t^10-378*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Oct 25 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^10)/(1-28*t+405*t^10-378*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 21 2016 *)

coxG[{10, 378, -27}] (* The coxG program is at A169452 *) (* G. C. Greubel, Oct 25 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-28*t+405*t^10-378*t^11)) \\ G. C. Greubel, Oct 25 2019

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-28*t+405*t^10-378*t^11) )); // G. C. Greubel, Oct 25 2019

(Sage)

def A166004_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^10)/(1-28*t+405*t^10-378*t^11)).list()

A166004_list(30) # G. C. Greubel, Oct 25 2019

(GAP) a:=[29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648426];; for n in [11..30] do a[n]:=27*Sum([1..9], j-> a[n-j]) - 378*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Oct 25 2019

CROSSREFS

Sequence in context: A164665 A164974 A165512 * A166423 A166616 A167082

Adjacent sequences:  A166001 A166002 A166003 * A166005 A166006 A166007

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)