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

Author

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

Keywords

• nonn

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).

Programs

Magma

R:=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

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 *)

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

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

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