A164332 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 47, 2162, 99452, 4574792, 210440432, 9680258791, 445291854660, 20483423028045, 942237354119580, 43342913451658140, 1993773796235517600, 91713584389960162440, 4218824411042032288125, 194065901246713684538250

Offset

0,2

Comments

The initial terms coincide with those of A170766, 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..600

Index entries for linear recurrences with constant coefficients, signature (45, 45, 45, 45, 45, -1035).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).

G.f.: (1+x)*(1-x^6)/(1 -46*x +1080*x^6 -1035*x^7). - G. C. Greubel, Apr 25 2019

a(n) = -1035*a(n-6) + 45*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 06 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7), {x, 0, 20}], x] (* G. C. Greubel, Sep 14 2017, modified Apr 25 2019 *)
coxG[{6, 1035, -45}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)) \\ G. C. Greubel, Sep 14 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Sequence in context: A162896 A163265 A163803 * A164692 A165179 A165703

Adjacent sequences: A164329 A164330 A164331 * A164333 A164334 A164335

Keyword

nonn

Author

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

Status

approved