A163453 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 19, 342, 6156, 110808, 1994373, 35895636, 646066215, 11628197676, 209289662676, 3766891838382, 67798255971825, 1220264268268608, 21962878883360919, 395298019772086050, 7114756005603413388

Offset

0,2

Comments

The initial terms coincide with those of A170738, 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..790

Index entries for linear recurrences with constant coefficients, signature (17,17,17,17,-153).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

a(n) = 17*a(n-1)+17*a(n-2)+17*a(n-3)+17*a(n-4)-153*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{17, 17, 17, 17, -153}, {1, 19, 342, 6156, 110808, 1994373}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 153, -17}] (* 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)/(1-18*x+170*x^5-153*x^6)) \\ G. C. Greubel, Dec 24 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6) )); // G. C. Greubel, May 13 2019
(SageMath) ((1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019

Crossrefs

Sequence in context: A162805 A049664 A163110 * A163968 A164631 A164909

Adjacent sequences: A163450 A163451 A163452 * A163454 A163455 A163456

Keyword

nonn,easy

Author

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

Status

approved