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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
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.
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
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved