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A163803
Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 47, 2162, 99452, 4574792, 210439351, 9680160420, 445285093005, 20483009107740, 942213581113500, 43341602191631640, 1993703464046530125, 91709888457205975050, 4218633208251709753275, 194056131188825472581550
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170766, although the two sequences are eventually different.
Computed with Magma using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
a(n) = 45*a(n-1)+45*a(n-2)+45*a(n-3)+45*a(n-4)-1035*a(n-5). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 04 2017 *)
coxG[{5, 1035, -45}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 09 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6)) \\ G. C. Greubel, Aug 04 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6) )); // G. C. Greubel, Aug 09 2019
(SageMath)
def A163803_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6)).list()
A163803_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[47, 2162, 99452, 4574792, 210439351];; for n in [6..30] do a[n]:=45*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1035*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019
CROSSREFS
Sequence in context: A189173 A162896 A163265 * A164332 A164692 A165179
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved