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A166308 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 5
1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645444551, 1993775131690399620, 91713656057756096205, 4218828178656675254940, 194066096218202223884700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170766, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).

FORMULA

G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).

G.f.: (1+x)*(1-x^10)/(1 -46*x +1080*x^10 -1035*x^11). - G. C. Greubel, Apr 25 2019

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11), {x, 0, 20}], x] (* G. C. Greubel, May 09 2016, modified Apr 25 2019 *)

coxG[{10, 1035, -45}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 07 2017 *)

PROG

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1-46*x+1080*x^10 -1035*x^11)) \\ G. C. Greubel, Apr 25 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11) )); // G. C. Greubel, Apr 25 2019

(Sage) ((1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

CROSSREFS

Sequence in context: A164692 A165179 A165703 * A166441 A166740 A167100

Adjacent sequences:  A166305 A166306 A166307 * A166309 A166310 A166311

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 03 2009

STATUS

approved

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Last modified July 9 05:17 EDT 2020. Contains 335538 sequences. (Running on oeis4.)