A163593 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 34, 1122, 37026, 1221858, 40320753, 1330566336, 43908078720, 1448946455616, 47814568344576, 1577858820890352, 52068617261591040, 1718240483647446528, 56701147733816154624, 1871111864101388705280, 61745833160498214613248

Offset

0,2

Comments

The initial terms coincide with those of A170753, 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..655

Index entries for linear recurrences with constant coefficients, signature (32, 32, 32, 32, -528).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).

a(n) = 32*a(n-1)+32*a(n-2)+32*a(n-3)+32*a(n-4)-528*a(n-5). - Wesley Ivan Hurt, May 11 2021

Mathematica

coxG[{5, 528, -32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 04 2016 *)
CoefficientList[Series[(1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)) \\ G. C. Greubel, Jul 29 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A214241 A162838 A163217 * A164050 A164670 A165166

Adjacent sequences: A163590 A163591 A163592 * A163594 A163595 A163596

Keyword

nonn

Author

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

Status

approved