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A164590 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I. 1
1, 11, 110, 1100, 11000, 110000, 1100000, 10999945, 109998900, 1099983555, 10999781100, 109997266500, 1099967220000, 10999617750000, 109995633002970, 1099950885086625, 10999454401704780, 109993999528128375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003953, 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..995

Index entries for linear recurrences with constant coefficients, signature (9,9,9,9,9,9,-45).

FORMULA

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 28 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8), {t, 0, 30}], t] (* G. C. Greubel, Aug 12 2017 *)

coxG[{7, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 28 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8)) \\ G. C. Greubel, Aug 12 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8) )); // G. C. Greubel, Aug 28 2019

(Sage)

def A164590_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8)).list()

A164590_list(30) # G. C. Greubel, Aug 28 2019

(GAP) a:=[11, 110, 1100, 11000, 110000, 1100000, 10999945];; for n in [8..30] do a[n]:=9*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -45*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Aug 28 2019

CROSSREFS

Sequence in context: A163404 A115808 A163955 * A115806 A115830 A164780

Adjacent sequences:  A164587 A164588 A164589 * A164591 A164592 A164593

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 30 14:40 EDT 2020. Contains 338079 sequences. (Running on oeis4.)