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A163958 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 13, 156, 1872, 22464, 269568, 3234738, 38815920, 465779886, 5589224784, 67069091232, 804809820672, 9657486564726, 115887063443580, 1390611458122458, 16686937868633604, 200238458992414128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170732, 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..920

Index entries for linear recurrences with constant coefficients, signature (11,11,11,11,11,-66).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(66*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-12*t+77*t^6-66*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-12*t+77*t^6-66*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)

coxG[{6, 66, -11}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 11 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-12*t+77*t^6-66*t^7)) \\ G. C. Greubel, Aug 13 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-12*t+77*t^6-66*t^7) )); // G. C. Greubel, Aug 11 2019

(Sage)

def A163878_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-12*t+77*t^6-66*t^7)).list()

A163878_list(30) # G. C. Greubel, Aug 11 2019

(GAP) a:=[13, 156, 1872, 22464, 269568, 3234738];; for n in [7..30] do a[n]:=11*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -66*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019

CROSSREFS

Sequence in context: A097827 A163084 A163438 * A164610 A164815 A165269

Adjacent sequences:  A163955 A163956 A163957 * A163959 A163960 A163961

KEYWORD

nonn,changed

AUTHOR

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

STATUS

approved

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Last modified August 23 14:06 EDT 2019. Contains 326231 sequences. (Running on oeis4.)