A163552 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 30, 870, 25230, 731670, 21217995, 615309240, 17843602560, 517453877640, 15005855150160, 435160887802830, 12619407316577880, 365955317872798920, 10612486887830912280, 307755817292235608520, 8924735934026717183820

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..696
• Index entries for linear recurrences with constant coefficients, signature (28, 28, 28, 28, -406).

Programs

Magma

I:=[1,30,870,25230,731670,21217995]; [n le 6 select I[n] else 28*Self(n-1)+28*Self(n-2)+28*Self(n-3)+28*Self(n-4)-406*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Apr 01 2017

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6) )); // G. C. Greubel, May 16 2019

Mathematica

CoefficientList[Series[(x^5+2*x^4+2*x^3+2*x^2+2*x+1)/(406*x^5-28*x^4 - 28*x^3-28*x^2-28*x+1), {x, 0, 20}], x] (* Wesley Ivan Hurt, Mar 31 2017 *)
LinearRecurrence[{28,28,28,28,-406}, {1,30,870,25230,731670,21217995}, 20] (* Vincenzo Librandi, Apr 01 2017 *)
coxG[{5, 406, -28}] (* 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)/(1-29*x+434*x^5-406*x^6)) \\ G. C. Greubel, Jul 28 2017

Sage

((1+x)*(1-x^5)/(1-29*x+434*x^5-406*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)/(406*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

a(n) = 28*a(n-1)+28*a(n-2)+28*a(n-3)+28*a(n-4)-406*a(n-5). - Wesley Ivan Hurt, May 11 2021