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A162983
Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
2
1, 10, 90, 810, 7245, 64800, 579600, 5184000, 46366380, 414707040, 3709193760, 33175513440, 296726124240, 2653957198080, 23737339710720, 212309865780480, 1898927161041600, 16984252473131520, 151909371770042880
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003952, 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)/(36*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 8*(a(n-1) + a(n-2) + a(n-3)) - 36*a(n-4).
G.f.: (1+x)*(1-x^4)/(1 - 9*x + 44*x^4 - 36*x^5). (End)
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5), {x, 0, 20}], x]
(* or *) coxG[{4, 36, -8}] (* 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)/(1-9*x+44*x^4-36*x^5)) \\ G. C. Greubel, Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[10, 90, 810, 7245];; for n in [5..20] do a[n]:=8*(a[n-1]+a[n-2] +a[n-3]) - 36*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
Sequence in context: A092420 A010579 A010576 * A163397 A163954 A164548
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved