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URL: https://oeis.org/A163215

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A163215
Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 32, 992, 30752, 952816, 29521920, 914703360, 28341043200, 878114994960, 27207394552800, 842990180666400, 26119092121336800, 809270367424023600, 25074322053313752000, 776899354951763496000, 24071343043338616536000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170751, 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)/(465*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 30*(a(n-1) + a(n-2) + a(n-3)) - 465*a(n-4).
G.f.: (1+x)*(1-x^4)/(1 - 31*x + 495*x^4 - 465*x^5). (End)
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(465*t^4-30*t^3-30*t^2 - 30*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{30, 30, 30, -465}, {1, 32, 992, 30752, 952816}, 20] (* G. C. Greubel, Dec 10 2016 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5) )); // G. C. Greubel, Apr 28 2019
(SageMath) ((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[32, 992, 30752, 952816];; for n in [5..20] do a[n]:=30*(a[n-1]+a[n-2] +a[n-3]) -465*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
Sequence in context: A264344 A228983 A162836 * A163565 A164036 A164668
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved