A162987 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 11, 110, 1100, 10945, 108900, 1083555, 10781100, 107269470, 1067306625, 10619454780, 105661128375, 1051303881870, 10460231387100, 104076892111005, 1035541095642900, 10303395297584895, 102516409155629700, 1020014649794722230, 10148910738927500925

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A003953, 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..995
• Index entries for linear recurrences with constant coefficients, signature (9,9,9,-45).

Programs

GAP

a:=[11,110,1100,10945];; for n in [5..20] do a[n]:=9*(a[n-1]+a[n-2] +a[n-3] -5*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5) )); // G. C. Greubel, Apr 28 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5), {x,0,20}], x] (* or *) coxG[{4, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)) \\ G. C. Greubel, Apr 28 2019

Sage

((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

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

a(n) = 9*(a(n-1) + a(n-2) + a(n-3) - 5*a(n-4)).

G.f.: (1+x)*(1-x^4)/(1 - 10*x + 54*x^4 - 45*x^5). (End)