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A164667
Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
2
1, 31, 930, 27900, 837000, 25110000, 753300000, 22598999535, 677969972100, 20339098744965, 610172949807900, 18305188118005500, 549155632253220000, 16474668628988250000, 494240048711397215760, 14827201156594414216125
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170750, 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)/(435*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 15 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2019 *)
coxG[{7, 435, -29}] (* 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)/(1-30*t+464*t^7-435*t^8)) \\ G. C. Greubel, Sep 15 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8) )); // G. C. Greubel, Sep 15 2019
(SageMath)
def A164667_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8)).list()
A164667_list(20) # G. C. Greubel, Sep 15 2019
(GAP) a:=[31, 930, 27900, 837000, 25110000, 753300000, 22598999535];; for n in [8..20] do a[n]:=29*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -435*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019
CROSSREFS
Sequence in context: A163214 A163564 A164030 * A164992 A165547 A166075
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved