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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 (list; graph; refs; listen; history; text; internal format)
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

G. C. Greubel, Table of n, a(n) for n = 0..600

Index entries for linear recurrences with constant coefficients, signature (43, 43, 43, -946).

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).

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

Adjacent sequences:  A163228 A163229 A163230 * A163232 A163233 A163234

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 2 16:02 EDT 2020. Contains 335404 sequences. (Running on oeis4.)