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A163835
Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 49, 2352, 112896, 5419008, 260111208, 12485281536, 599290805400, 28765828659456, 1380753535666176, 66275870193948072, 3181227392509145280, 152698224757140201048, 7329481664494083280704, 351813529958166317583360
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170768, 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)/(1128*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
a(n) = 47*a(n-1)+47*a(n-2)+47*a(n-3)+47*a(n-4)-1128*a(n-5). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 05 2017 *)
coxG[{5, 1128, -47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 10 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)) \\ G. C. Greubel, Aug 05 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A163835_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)).list()
A163835_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[49, 2352, 112896, 5419008, 260111208];; for n in [6..20] do a[n]:=47*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1128*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019
CROSSREFS
Sequence in context: A049682 A162914 A163287 * A164350 A164694 A165181
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved