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A163953 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 9, 72, 576, 4608, 36864, 294876, 2358720, 18867492, 150921792, 1207229184, 9656672256, 77244089580, 617878417968, 4942433025684, 39534710232528, 316239654648960, 2529613056079872, 20234471292326844, 161856307428494112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003951, 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..1000

Index entries for linear recurrences with constant coefficients, signature (7,7,7,7,7,-28).

FORMULA

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

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)

coxG[{6, 28, -7}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7)) \\ G. C. Greubel, Aug 13 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7) )); // G. C. Greubel, Aug 10 2019

(Sage)

def A163953_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7)).list()

A163953_list(30) # G. C. Greubel, Aug 10 2019

(GAP) a:=[9, 72, 576, 4608, 36864, 294876];; for n in [7..30] do a[n]:=7*(a[n-1]+a[n-2]+a[n-3]+a[n-4]+a[n-5]) -28*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019

CROSSREFS

Sequence in context: A129328 A162960 A163391 * A164375 A164777 A165216

Adjacent sequences:  A163950 A163951 A163952 * A163954 A163955 A163956

KEYWORD

nonn,changed

AUTHOR

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

STATUS

approved

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Last modified August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)