A164667 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 31, 930, 27900, 837000, 25110000, 753300000, 22598999535, 677969972100, 20339098744965, 610172949807900, 18305188118005500, 549155632253220000, 16474668628988250000, 494240048711397215760, 14827201156594414216125

Offset

0,2

Comments

The initial terms coincide with those of A170750, 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..670

Index entries for linear recurrences with constant coefficients, signature (29,29,29,29,29,29,-435).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 15 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2019 *)
coxG[{7, 435, -29}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 15 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8)) \\ G. C. Greubel, Sep 15 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8) )); // G. C. Greubel, Sep 15 2019
(Sage)
def A164667_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8)).list()
A164667_list(20) # G. C. Greubel, Sep 15 2019
(GAP) a:=[31, 930, 27900, 837000, 25110000, 753300000, 22598999535];; for n in [8..20] do a[n]:=29*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -435*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019

Crossrefs

Sequence in context: A163214 A163564 A164030 * A164992 A165547 A166075

Adjacent sequences: A164664 A164665 A164666 * A164668 A164669 A164670

Keyword

nonn

Author

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

Status

approved