A167935 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170741, 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Crossrefs

Cf. A154638, A170741.

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17) )); // G. C. Greubel, Apr 26 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17), {x, 0, 20}], x] (* G. C. Greubel, Jul 01 2016, modified Apr 26 2019 *)
coxG[{16, 210, -20}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17)) \\ G. C. Greubel, Apr 26 2019

Sage

((1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

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)/(210*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

G.f.: (1+x)*(1-x^16)/(1 - 21*x + 230*x^16 - 210*x^17). - G. C. Greubel, Apr 26 2019

a(n) = -210*a(n-16) + 20*Sum_{k=1..15} a(n-k). - Wesley Ivan Hurt, May 06 2021