A163548 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 28, 756, 20412, 551124, 14879970, 401748984, 10846947384, 292860149400, 7907023424664, 213484216161762, 5763927599870076, 155622096911221668, 4201690015605193020, 113442752267421552612, 3062876603036110993314

Offset

0,2

Comments

The initial terms coincide with those of A170747, 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..695

Index entries for linear recurrences with constant coefficients, signature (26, 26, 26, 26, -351).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

a(n) = 26*a(n-1)+26*a(n-2)+26*a(n-3)+26*a(n-4)-351*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 05 2018 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

Crossrefs

Sequence in context: A097834 A162830 A163187 * A164025 A164664 A164970

Adjacent sequences: A163545 A163546 A163547 * A163549 A163550 A163551

Keyword

nonn

Author

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

Status

approved