A164664 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773314, 292889869272, 7908026195160, 213516699839352, 5764950695053368, 155653663349994264, 4202648764205784984, 113471512684966713186, 3063730735882188973692

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 (26,26,26,26,26,26,-351).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 15 2019

Mathematica

CoefficientList[Series[(t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 20}], t] (* Wesley Ivan Hurt, Apr 25 2017 *)
coxG[{7, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 13 2018 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)) \\ G. C. Greubel, Sep 15 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8) )); // G. C. Greubel, Sep 15 2019
(SageMath)
def A164664_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)).list()
A164664_list(20) # G. C. Greubel, Sep 15 2019
(GAP) a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773314];; for n in [8..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -351*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019

Crossrefs

Cf. A154638, A170747.

Sequence in context: A163187 A163548 A164025 * A164970 A165456 A165980

Adjacent sequences: A164661 A164662 A164663 * A164665 A164666 A164667

Keyword

nonn

Author

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

Status

approved