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A165939
Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192008963, 610878224191620, 13439320932093441, 295665060503367324, 6504631331014936812, 143101889281027434912
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170742, 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 (21,21,21,21,21,21,21,21,21,-231).
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)/(231*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 25 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 18 2016 *)
coxG[{10, 231, -21}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 25 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11)) \\ G. C. Greubel, Sep 25 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11) )); // G. C. Greubel, Sep 25 2019
(Sage)
def A165939_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11)).list()
A165939_list(30) # G. C. Greubel, Sep 25 2019
(GAP) a:=[23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192008963];; for n in [11..30] do a[n]:=21*Sum([1..9], j-> a[n-j]) -231*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 25 2019
CROSSREFS
Sequence in context: A164636 A164957 A165365 * A166417 A166610 A167076
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved