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A166368
Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1
1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867843965, 313810595280, 2824295353920, 25418658152880, 228767923084320, 2058911305134480, 18530201722590720, 166771815290740080
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003952, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 8*Sum_{j=1..10} a(n-j) - 36*a(n-11).
G.f.: (1+t)*(1 - t^11)/(1 - 9*t + 44*t^11 - 36*t^12). (End)
MAPLE
seq(coeff(series((1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 14 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 36, -8}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 14 2020 *)
PROG
(Sage)
def A166368_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12) ).list()
A166368_list(30) # G. C. Greubel, Mar 14 2020
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-9*x+44*x^16-36*x^17) )); // G. C. Greubel, Jul 23 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved