A167962 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750

Offset: 0

Author

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

Keywords

• nonn

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..500
• Index entries for linear recurrences with constant coefficients, signature (44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,-990).

Crossrefs

Cf. A154638, A169452, A170765.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-45*x+1034*x^16-990*x^17) )); // G. C. Greubel, Jan 17 2023

Mathematica

CoefficientList[Series[(1+t)*(1-t^16)/(1-45*t+1034*t^16-990*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 03 2016 *)
coxG[{16,990,-44,40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jan 17 2023 *)

SageMath

def A167962_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-45*x+1034*x^16-990*x^17) ).list()
A167962_list(40) # G. C. Greubel, Jan 17 2023

Formula

G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 990*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

From G. C. Greubel, Jan 17 2023: (Start)

a(n) = Sum_{j=1..15} a(n-j) - 990*a(n-16).

G.f.: (1+x)*(1-x^16)/(1 - 45*x + 1034*x^16 - 990*x^17). (End)