A162889 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 46, 2070, 92115, 4098600, 182342160, 8112199590, 360902223000, 16056115855560, 714317717862540, 31779155482826400, 1413817266133308960, 62899068010426041240, 2798305588240613272800, 124493325781573753947360

Offset

0,2

Comments

The initial terms coincide with those of A170765, 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..605

Index entries for linear recurrences with constant coefficients, signature (44, 44, -990).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(990*t^3 - 44*t^2 - 44*t + 1).

From G. C. Greubel, Apr 28 2019: (Start)

a(n) = 44*a(n-1) + 44*a(n-2) - 990*a(n-3).

G.f.: (1+x)*(1-x^3)/(1 - 45*x + 1034*x^3 - 990*x^4). (End)

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 990, -44}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1))); // G. C. Greubel, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1-45*x+1034*x^3-990*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[46, 2070, 92115];; for n in [4..20] do a[n]:=44*a[n-1]+44*a[n-2] - 990*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A331707 A223813 A324451 * A163232 A163802 A164331

Adjacent sequences: A162886 A162887 A162888 * A162890 A162891 A162892

Keyword

nonn

Author

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

Status

approved