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A163208
Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 30, 870, 25230, 731235, 21193200, 614237400, 17802288000, 515959239390, 14953916974920, 433405617680280, 12561286100120520, 364060598322527820, 10551476830837383840, 305810801346502707360, 8863237603561904401440
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170749, 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)/(406*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 28*(a(n-1) + a(n-2) + a(n-3)) - 406*a(n-4).
G.f.: (1+x)*(1-x^4)/(1 - 29*x + 434*x^4 - 406*x^5). (End)
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(406*t^4-28*t^3-28*t^2- 28*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{28, 28, 28, -406}, {1, 30, 870, 25230, 731235}, 20] (* G. C. Greubel, Dec 10 2016 *)
coxG[{4, 406, -28}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-29*x+434*x^4-406*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)/(1-29*x+434*x^4-406*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-29*x+434*x^4-406*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[30, 870, 25230, 731235];; for n in [5..20] do a[n]:=28*(a[n-1] + a[n-2]+a[n-3]) -406*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
Sequence in context: A367333 A007850 A162833 * A163552 A164027 A164666
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved