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A163265
Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 47, 2162, 99452, 4573711, 210340980, 9673398765, 444871172700, 20459237269140, 940902479912925, 43271284508242650, 1990008638480367675, 91518761835509986350, 4208868045065726973000, 193562170919821248573375
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^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*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)-1035*a(n-4). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3-45*t^2 - 45*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {45, 45, 45, -1035}, {47, 2162, 99452, 4573711}, 20] (* G. C. Greubel, Dec 12 2016 *)
coxG[{4, 1035, -45}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3- 45*t^2-45*t+1)) \\ G. C. Greubel, Dec 12 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5) )); // G. C. Greubel, May 01 2019
(Sage) ((1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019
(GAP) a:=[47, 2162, 99452, 4573711];; for n in [5..20] do a[n]:=45*(a[n-1]+a[n-2] +a[n-3]-23*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, May 01 2019
CROSSREFS
Sequence in context: A289984 A189173 A162896 * A163803 A164332 A164692
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved