A163397 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 10, 90, 810, 7290, 65565, 589680, 5303520, 47699280, 429001920, 3858394860, 34701968160, 312105587040, 2807042441760, 25246223065440, 227061682284240, 2042167156174080, 18367021030590720, 165190915209012480

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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..1000

Index entries for linear recurrences with constant coefficients, signature (8, 8, 8, 8, -36).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

a(n) = 8*a(n-1)+8*a(n-2)+8*a(n-3)+8*a(n-4)-36*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, 8, 8, 8, -36}, {1, 10, 90, 810, 7290, 65565}, 30] (* G. C. Greubel, Dec 21 2016 *)
coxG[{5, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)) \\ G. C. Greubel, Dec 21 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Crossrefs

Sequence in context: A010579 A010576 A162983 * A163954 A164548 A164779

Adjacent sequences: A163394 A163395 A163396 * A163398 A163399 A163400

Keyword

nonn

Author

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

Status

approved