A163993 - OEIS

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A163993

Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 25, 600, 14400, 345600, 8294400, 199065300, 4777560000, 114661267500, 2751866280000, 66044691360000, 1585070208000000, 38041627760729700, 912997692709095600, 21911911659905871900, 525885088676233035600

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170744, 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..720

Index entries for linear recurrences with constant coefficients, signature (23, 23, 23, 23, 23, -276).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(276*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

G.f.: (1+x)*(1-x^7)/(1 -24*x +299*x^6 -276*x^7). - G. C. Greubel, Apr 25 2019

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7), {x, 0, 20}], x] (* G. C. Greubel, Aug 24 2017, modified Apr 25 2019 *)

coxG[{6, 276, -23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 02 2018 *)

PROG

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7)) \\ G. C. Greubel, Aug 24 2017, modified Apr 25 2019

(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7) )); // G. C. Greubel, Apr 25 2019

(Sage) ((1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

CROSSREFS

Sequence in context: A162811 A163175 A163525 * A164638 A164963 A165368

Adjacent sequences: A163990 A163991 A163992 * A163994 A163995 A163996

KEYWORD

nonn

AUTHOR

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

STATUS

approved