A163208 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 30, 870, 25230, 731235, 21193200, 614237400, 17802288000, 515959239390, 14953916974920, 433405617680280, 12561286100120520, 364060598322527820, 10551476830837383840, 305810801346502707360, 8863237603561904401440

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

G. C. Greubel, Table of n, a(n) for n = 0..680

Index entries for linear recurrences with constant coefficients, signature (28, 28, 28, -406).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(406*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

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

a(n) = 28*(a(n-1) + a(n-2) + a(n-3)) - 406*a(n-4).

G.f.: (1+x)*(1-x^4)/(1 - 29*x + 434*x^4 - 406*x^5). (End)

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(406*t^4-28*t^3-28*t^2- 28*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{28, 28, 28, -406}, {1, 30, 870, 25230, 731235}, 20] (* G. C. Greubel, Dec 10 2016 *)
coxG[{4, 406, -28}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-29*x+434*x^4-406*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-29*x+434*x^4-406*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-29*x+434*x^4-406*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[30, 870, 25230, 731235];; for n in [5..20] do a[n]:=28*(a[n-1] + a[n-2]+a[n-3]) -406*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A367333 A007850 A162833 * A163552 A164027 A164666

Adjacent sequences: A163205 A163206 A163207 * A163209 A163210 A163211

Keyword

nonn,easy

Author

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

Status

approved