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

0,2

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).

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

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 *)

Prog

(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<x>:=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
(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

Crossrefs

Sequence in context: A007850 A162833 A163208 * A164027 A164666 A164983

Adjacent sequences: A163549 A163550 A163551 * A163553 A163554 A163555

Keyword

nonn

Author

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

Status

approved