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A163230
Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 44, 1892, 81356, 3497362, 150345888, 6463124976, 277839201024, 11943854101410, 513446807614356, 22072240836651852, 948849634132915284, 40789498214388049434, 1753474001285744132472, 75378987430163637459624
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170763, 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)/(903*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
a(n) = 42*a(n-1)+42*a(n-2)+42*a(n-3)-903*a(n-4). - Wesley Ivan Hurt, May 06 2021
MATHEMATICA
coxG[{4, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 18 2015 *)
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3-42*t^2 - 42*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {42, 42, 42, -903}, {44, 1892, 81356, 3497362}, 50]] (* G. C. Greubel, Dec 11 2016 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3 - 42*t^2-42*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019
CROSSREFS
Sequence in context: A278793 A004295 A162882 * A163748 A164277 A164688
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved