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A165965
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Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
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1
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1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663874836, 994236269114880, 22867434189496512, 525950986355068032, 12096872686089474624, 278228071778284843776
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OFFSET
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0,2
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COMMENTS
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The initial terms coincide with those of A170743, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (22,22,22,22,22,22,22,22,22,-253).
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FORMULA
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G.f.: (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)/(253*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 26 2019
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 18 2016 *)
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PROG
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(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11)) \\ G. C. Greubel, Sep 26 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11) )); // G. C. Greubel, Sep 26 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11)).list()
(GAP) a:=[24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663874836];; for n in [11..30] do a[n]:=22*Sum([1..9], j-> a[n-j]) -253*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 26 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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