A163266 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 48, 2256, 106032, 4982376, 234118656, 11001086208, 516933992448, 24290397127896, 1141390199234256, 53633194222120752, 2520189436004377296, 118422087020288430408, 5564578001118314478240, 261475955285477822620512

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, -1081).

Formula

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

a(n) = 46*a(n-1)+46*a(n-2)+46*a(n-3)-1081*a(n-4). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1081*t^4-46*t^3-46*t^2 - 46*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {46, 46, 46, -1081}, {48, 2256, 106032, 4982376}, 20] (* G. C. Greubel, Dec 12 2016 *)
coxG[{4, 1081, -46}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1081*t^4-46*t^3 - 46*t^2-46*t+1)) \\ G. C. Greubel, Dec 12 2016 *)
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-47*x+1127*x^4-1081*x^5) )); // G. C. Greubel, May 01 2019
(Sage) ((1+x)*(1-x^4)/(1-47*x+1127*x^4-1081*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019
(GAP) a:=[48, 2256, 106032, 4982376];; for n in [5..20] do a[n]:=46*(a[n-1] +a[n-2] +a[n-3]) -1081*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, May 01 2019

Crossrefs

Sequence in context: A049678 A162913 A156093 * A163829 A164348 A164693

Adjacent sequences: A163263 A163264 A163265 * A163267 A163268 A163269

Keyword

nonn

Author

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

Status

approved