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A163432 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 12, 132, 1452, 15972, 175626, 1931160, 21234840, 233496120, 2567499000, 28231951770, 310435603500, 3413517587700, 37534684133100, 412727480315700, 4538308419052650, 49902767052699000, 548725632894681000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003954, 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..950

Index entries for linear recurrences with constant coefficients, signature (10, 10, 10, 10, -55).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, 10, 10, 10, -55}, {1, 12, 132, 1452, 15972, 175626}, 30] (* G. C. Greubel, Dec 23 2016 *)

coxG[{5, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6)) \\ G. C. Greubel, Dec 23 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6) )); // G. C. Greubel, May 12 2019

(Sage) ((1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

CROSSREFS

Sequence in context: A010580 A010577 A163055 * A163957 A063813 A164601

Adjacent sequences:  A163429 A163430 A163431 * A163433 A163434 A163435

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified January 20 23:24 EST 2020. Contains 331104 sequences. (Running on oeis4.)