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A166026
Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379275635, 12621216998980800, 366015292970077800, 10614443496121659600, 307818861387220827000, 8926746980220492242400
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170749, 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 (28,28,28,28,28,28,28,28,28,-406).
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)/(406*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Dec 05 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 21 2016 *)
coxG[{10, 406, -28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 13 2020 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)) \\ G. C. Greubel, Dec 05 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11) )); // G. C. Greubel, Dec 05 2019
(Sage)
def A166026_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)).list()
A166026_list(30) # G. C. Greubel, Dec 05 2019
(GAP) a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379275635];; for n in [11..30] do a[n]:=28*Sum([1..9], j-> a[n-j]) - 406*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Dec 05 2019
CROSSREFS
Sequence in context: A164666 A164983 A165515 * A166424 A166617 A167083
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved