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

Author

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

Keywords

• nonn
• easy

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).

Programs

Magma

R:=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

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 *)

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

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

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