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A165757
Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310710, 5242800, 20971050, 83883600, 335532000, 1342118400, 5368435200, 21473587200, 85893734400, 343572480000, 1374280089690, 5497081037820, 21988166868630, 87952038348420
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003947, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
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)/(6*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 17 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 07 2016 *)
coxG[{10, 6, -3}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 17 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11)) \\ G. C. Greubel, Sep 17 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11) )); // G. C. Greubel, Sep 17 2019
(Sage)
def A165757_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11)).list()
A165757_list(30) # G. C. Greubel, Sep 17 2019
(GAP) a:=[5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310710];; for n in [11..30] do a[n]:=3*Sum([1..9], j-> a[n-j]) -6*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 17 2019
CROSSREFS
Sequence in context: A164354 A164706 A165185 * A166331 A166495 A166859
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved