A163452 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 18, 306, 5202, 88434, 1503225, 25552224, 434343744, 7383094560, 125499873024, 2133281378232, 36262103930496, 616393221671808, 10477621608796800, 178101495469706112, 3027418232198243904, 51460888233840150528

Offset

0,2

Comments

The initial terms coincide with those of A170737, 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..800

Index entries for linear recurrences with constant coefficients, signature (16, 16, 16, 16, -136).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

a(n) = 16*a(n-1)+16*a(n-2)+16*a(n-3)+16*a(n-4)-136*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6), {x, 0, 20}], x] (* or *)  LinearRecurrence[{16, 16, 16, 16, -136}, {1, 18, 306, 5202, 88434, 1503225}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 136, -16}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6)) \\ G. C. Greubel, Dec 24 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6) )); // G. C. Greubel, May 13 2019
(Sage) ((1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019

Crossrefs

Sequence in context: A097831 A342885 A163104 * A163967 A164630 A164892

Adjacent sequences: A163449 A163450 A163451 * A163453 A163454 A163455

Keyword

nonn

Author

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

Status

approved