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A164330
Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
2
1, 45, 1980, 87120, 3833280, 168664320, 7421229090, 326534036400, 14367495685950, 632169725893200, 27815464230602400, 1223880262963776000, 53850724390367020710, 2369431557254469630780, 104254974618644628784170
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.
LINKS
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -44*x +989*x^6 -946*x^7). - G. C. Greubel, Apr 25 2019
a(n) = -946*a(n-6) + 43*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 06 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7), {x, 0, 20}], x] (* G. C. Greubel, Sep 14 2017, modified Apr 25 2019 *)
coxG[{6, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)) \\ G. C. Greubel, Sep 14 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A162885 A163231 A163749 * A164690 A165177 A165699
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved