A163829 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 48, 2256, 106032, 4983504, 234223560, 11008454304, 517394861664, 24317441438880, 1142914245838944, 53716710971646072, 2524673262335033136, 118659072125876564688, 5576949543463542381360, 262115366765585626863312

Offset

0,2

Comments

The initial terms coincide with those of A170767, 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..595

Index entries for linear recurrences with constant coefficients, signature (46, 46, 46, 46, -1081).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

G.f.: (1+x)*(1-x^5)/(1 -47*x +1127*x^5 -1081*x^6). - G. C. Greubel, Apr 25 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 05 2017, modified Apr 25 2019 *)
coxG[{5, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 16 2025 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6)) \\ G. C. Greubel, Aug 05 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6) )); // G. C. Greubel, Apr 25 2019
(SageMath) ((1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Sequence in context: A162913 A156093 A163266 * A164348 A164693 A165180

Adjacent sequences: A163826 A163827 A163828 * A163830 A163831 A163832

Keyword

nonn

Author

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

Status

approved