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A164348 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 2
1, 48, 2256, 106032, 4983504, 234224688, 11008559208, 517402229760, 24317902308096, 1142941291421184, 53718235195007232, 2524756795581284352, 118663557238871024856, 5577186619014877732560, 262127744246735162576688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170767, 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..595

Index entries for linear recurrences with constant coefficients, signature (46, 46, 46, 46, 46, -1081).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 24 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2017 *)

coxG[{6, 1081, -46}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 24 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)) \\ G. C. Greubel, Sep 15 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7) )); // G. C. Greubel, Aug 24 2019

(Sage)

def A164348_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)).list()

A164348_list(20) # G. C. Greubel, Aug 24 2019

(GAP) a:=[48, 2256, 106032, 4983504, 234224688, 11008559208];; for n in [7..20] do a[n]:=46*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1081*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019

CROSSREFS

Sequence in context: A156093 A163266 A163829 * A164693 A165180 A165708

Adjacent sequences:  A164345 A164346 A164347 * A164349 A164350 A164351

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 16 13:35 EDT 2020. Contains 335788 sequences. (Running on oeis4.)