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A165894
Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10751999999790, 215039999991600, 4300799999748210, 86015999993288400, 1720319999832252000, 34406399995974720000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170740, 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 (19,19,19,19,19,19,19,19,19,-190).
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)/(190*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 24 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 190, -19}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 24 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11)) \\ G. C. Greubel, Sep 24 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11) )); // G. C. Greubel, Sep 24 2019
(Sage)
def A165894_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11)).list()
A165894_list(30) # G. C. Greubel, Sep 24 2019
(GAP) a:=[21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10751999999790];; for n in [7..30] do a[n]:=19*Sum([1..9], j-> a[n-j]) -190*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019
CROSSREFS
Sequence in context: A164634 A164954 A165358 * A166415 A166603 A167074
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved