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A163439 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 14, 182, 2366, 30758, 399763, 5195736, 67529280, 877681896, 11407280976, 148261073142, 1926957516120, 25044775341768, 325508355356184, 4230650423530440, 54986001777229068, 714656161291232160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170733, 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..895

Index entries for linear recurrences with constant coefficients, signature (12, 12, 12, 12, -78).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(78*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^5)/(1-13*x+90*x^5-78*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{12, 12, 12, 12, -78}, {1, 14, 182, 2366, 30758, 399763}, 30]] (* G. C. Greubel, Dec 23 2016 *)

coxG[{5, 78, -12}] (* 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)/(1-13*x+90*x^5-78*x^6)) \\ G. C. Greubel, Dec 23 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-13*x+90*x^5-78*x^6) )); // G. C. Greubel, May 12 2019

(Sage) ((1+x)*(1-x^5)/(1-13*x+90*x^5-78*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

CROSSREFS

Sequence in context: A097828 A030008 A163090 * A163959 A164618 A164835

Adjacent sequences:  A163436 A163437 A163438 * A163440 A163441 A163442

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 12 22:46 EDT 2020. Contains 335669 sequences. (Running on oeis4.)