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A163802
Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 46, 2070, 93150, 4191750, 188627715, 8488200600, 381966932160, 17188417679400, 773474553522000, 34806164017265190, 1566268790718951000, 70481709031863535560, 3171659511757241439000, 142723895272921025613000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170765, 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)/(990*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
a(n) = 44*a(n-1)+44*a(n-2)+44*a(n-3)+44*a(n-4)-990*a(n-5). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 04 2017 *)
coxG[{5, 990, -44}] (* 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)/(1-45*t+1034*t^5-990*t^6)) \\ G. C. Greubel, Aug 04 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6) )); // G. C. Greubel, Aug 09 2019
(SageMath)
def A163802_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6)).list()
A163802_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[46, 2070, 93150, 4191750, 188627715];; for n in [6..30] do a[n]:=44*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -990*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019
CROSSREFS
Sequence in context: A324451 A162889 A163232 * A164331 A164691 A165178
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved