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A166075
Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535, 18305189999972100, 549155699998744965, 16474670999949807900, 494240129998118005500, 14827203899932253220000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170750, 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 (29,29,29,29,29,29,29,29,29,-435).
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)/(435*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Dec 05 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 24 2016 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)) \\ G. C. Greubel, Dec 05 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11) )); // G. C. Greubel, Dec 05 2019
(Sage)
def A166075_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)).list()
A166075_list(30) # G. C. Greubel, Dec 05 2019
(GAP) a:=[31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535];; for n in [11..30] do a[n]:=29*Sum([1..9], j-> a[n-j]) - 435*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Dec 05 2019
CROSSREFS
Sequence in context: A164667 A164992 A165547 * A166425 A166618 A167084
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved