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A164610 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I. 1
1, 13, 156, 1872, 22464, 269568, 3234816, 38817714, 465811632, 5589728430, 67076607312, 804917681568, 9658992904704, 115907683567104, 1390889427339126, 16690639822542972, 200287278204994266 (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 (11,11,11,11,11,11,-66).

FORMULA

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(66*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).

a(n) = -66*a(n-7) + 11*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021

MAPLE

seq(coeff(series((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 15 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8), {t, 0, 20}], t] (* G. C. Greubel, Aug 10 2017 *)

coxG[{7, 6, -11}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 15 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8)) \\ G. C. Greubel, Aug 10 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8) )); // G. C. Greubel, Sep 15 2019

(Sage)

def A164610_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8)).list()

A164610_list(20) # G. C. Greubel, Sep 15 2019

(GAP) a:=[13, 156, 1872, 22464, 269568, 3234816, 38817714];; for n in [8..20] do a[n]:=11*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -66*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019

CROSSREFS

Sequence in context: A163084 A163438 A163958 * A164815 A165269 A165873

Adjacent sequences:  A164607 A164608 A164609 * A164611 A164612 A164613

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified June 18 23:16 EDT 2021. Contains 345125 sequences. (Running on oeis4.)