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A164670
Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
2
1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910385, 1449027024192, 47817891187968, 1577990389060800, 52073682174315648, 1718431489817621568, 56708238440133282816, 1871371844637407092464, 61755270084763733187072
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170753, 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)/(528*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 15 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2019 *)
coxG[{7, 528, -32}] (* 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)/(1-33*t+560*t^7-528*t^8)) \\ G. C. Greubel, Sep 15 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8) )); // G. C. Greubel, Sep 15 2019
(Sage)
def A164670_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8)).list()
A164670_list(20) # G. C. Greubel, Sep 15 2019
(GAP) a:=[34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910385];; for n in [8..20] do a[n]:=32*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -528*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019
CROSSREFS
Sequence in context: A163217 A163593 A164050 * A165166 A165649 A166130
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved