A164025 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 28, 756, 20412, 551124, 14880348, 401769018, 10847753280, 292889063376, 7907997281184, 213515725982832, 5764919185089792, 155652671753506746, 4202618188762620900, 113470584484975272828, 3063702902583418604964

Offset

0,2

Comments

The initial terms coincide with those of A170747, 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..695

Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,-351).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

a(n) = -351*a(n-6) + 26*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *)
coxG[{6, 351, -26}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7)) \\ G. C. Greubel, Sep 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164025_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7)).list()
A164025_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[28, 756, 20412, 551124, 14880348, 401769018];; for n in [7..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -351*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019

Crossrefs

Sequence in context: A162830 A163187 A163548 * A164664 A164970 A165456

Adjacent sequences: A164022 A164023 A164024 * A164026 A164027 A164028

Keyword

nonn

Author

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

Status

approved