A163219 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 36, 1260, 44100, 1542870, 53978400, 1888472880, 66069561600, 2311490430270, 80869130653500, 2829263840578980, 98983800307381500, 3463018394666864670, 121156152466965222600, 4238733846520797445080, 148295107229819712107400

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170755, 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..645
• Index entries for linear recurrences with constant coefficients, signature (34, 34, 34, -595).

Crossrefs

Cf. A154638, A170755.

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-35*x+629*x^4-595*x^5) )); // G. C. Greubel, Apr 30 2019

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(595*t^4-34*t^3-34*t^2 - 34*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[{34, 34, 34, -595}, {36, 1260, 44100, 1542870}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 595, -34}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)

PARI

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(595*t^4-34*t^3 - 34*t^2-34*t+1)) \\ G. C. Greubel, Dec 11 2016

Sage

((1+x)*(1-x^4)/(1-35*x+629*x^4-595*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

a(n) = -595*a(n-4) + 34*Sum_{k=1..3} a(n-k). - Wesley Ivan Hurt, May 05 2021