A163440 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 15, 210, 2940, 41160, 576135, 8064420, 112881405, 1580053020, 22116729180, 309578036040, 4333306233165, 60655281460410, 849019887139515, 11884122064943310, 166347525415813560, 2328442863574420320

Offset

0,2

Comments

The initial terms coincide with those of A170734, 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..855

Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, -91).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).

a(n) = 13*a(n-1)+13*a(n-2)+13*a(n-3)+13*a(n-4)-91*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, 13, 13, 13, -91}, {15, 210, 2940, 41160, 576135}, 30] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 91, -13}] (* 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)/(1-14*x+104*x^5-91*x^6)) \\ G. C. Greubel, Dec 23 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Crossrefs

Sequence in context: A162785 A076139 A163091 * A163962 A164626 A164860

Adjacent sequences: A163437 A163438 A163439 * A163441 A163442 A163443

Keyword

nonn

Author

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

Status

approved