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A163231
Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 45, 1980, 87120, 3832290, 168577200, 7415481150, 326196882000, 14348955088710, 631190926398780, 27765226324720170, 1221354364616557380, 53725709508796162530, 2363320544672336677560, 103959241263364038810390
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170764, 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)/(946*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
a(n) = 43*a(n-1)+43*a(n-2)+43*a(n-3)-946*a(n-4). - Wesley Ivan Hurt, May 06 2021
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3-43*t^2 - 43*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {43, 43, 43, -946}, {45, 1980, 87120, 3832290}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3 - 43*t^2-43*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019
CROSSREFS
Sequence in context: A203828 A318221 A162885 * A163749 A164330 A164690
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved