A164030 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 31, 930, 27900, 837000, 25110000, 753299535, 22598972100, 677968744965, 20339049807900, 610171118005500, 18305122253220000, 549153328988465760, 16474589711416216125, 494237386595541683490, 14827112455463543698875

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..675

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

Formula

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

a(n) = -435*a(n-6) + 29*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

Mathematica

coxG[{6, 435, -29}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 29 2016 *)
CoefficientList[Series[(1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7)) \\ G. C. Greubel, Sep 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164030_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7)).list()
A164030_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[31, 930, 27900, 837000, 25110000, 753299535];; for n in [7..30] do a[n]:=29*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -435*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019

Crossrefs

Sequence in context: A162835 A163214 A163564 * A164667 A164992 A165547

Adjacent sequences: A164027 A164028 A164029 * A164031 A164032 A164033

Keyword

nonn

Author

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

Status

approved