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A164277 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 44, 1892, 81356, 3498308, 150427244, 6468370546, 278139892800, 11960013642192, 514280511441312, 22114058759539824, 950904387665438976, 40888882692839511330, 1758221698790838894228, 75603521996953503778764 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170763, 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..610

Index entries for linear recurrences with constant coefficients, signature (42,42,42,42,42,-903).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

a(n) = -903*a(n-6) + 42*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 16 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 12 2017 *)

coxG[{6, 903, -42}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 16 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7)) \\ G. C. Greubel, Sep 12 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7) )); // G. C. Greubel, Aug 16 2019

(Sage)

def A164277_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7)).list()

A164277_list(30) # G. C. Greubel, Aug 16 2019

(GAP) a:=[44, 1892, 81356, 3498308, 150427244, 6468370546];; for n in [7..30] do a[n]:=42*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -903*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 16 2019

CROSSREFS

Sequence in context: A162882 A163230 A163748 * A164688 A165176 A165695

Adjacent sequences:  A164274 A164275 A164276 * A164278 A164279 A164280

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)