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A165876
Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093749880, 9226406246400, 138396093669120, 2075941404633600, 31139121063456000, 467086815861120000, 7006302236556000000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170735, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (14,14,14,14,14,14,14,14,14,-105).
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)/(105*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 23 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 105, -14}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11)) \\ G. C. Greubel, Aug 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A165876_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11)).list()
A165876_list(20) # G. C. Greubel, Aug 10 2019
(GAP) a:=[16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093749880];; for n in [11..20] do a[n]:=14*Sum([1..9], j-> a[n-j]) -105*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A164867 A063814 A165308 * A166410 A166584 A167026
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved