A163549 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 29, 812, 22736, 636608, 17824618, 499077936, 13973864310, 391259299536, 10955011154976, 306733334006862, 8588337963333660, 240467992209756738, 6732950603977585764, 188518328027869860720, 5278393098774299901978

Offset

0,2

Comments

The initial terms coincide with those of A170748, 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..685

Index entries for linear recurrences with constant coefficients, signature (27, 27, 27, 27, -378).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

a(n) = 27*a(n-1)+27*a(n-2)+27*a(n-3)+27*a(n-4)-378*a(n-5). - Wesley Ivan Hurt, May 11 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 378, -27}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

Crossrefs

Sequence in context: A159669 A162831 A163207 * A164026 A164665 A164974

Adjacent sequences: A163546 A163547 A163548 * A163550 A163551 A163552

Keyword

nonn,easy

Author

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

Status

approved