A166368 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867843965, 313810595280, 2824295353920, 25418658152880, 228767923084320, 2058911305134480, 18530201722590720, 166771815290740080

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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..500

Index entries for linear recurrences with constant coefficients, signature (8,8,8,8,8,8,8,8,8,8,-36).

Formula

G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

From G. C. Greubel, Jul 23 2024: (Start)

a(n) = 8*Sum_{j=1..10} a(n-j) - 36*a(n-11).

G.f.: (1+t)*(1 - t^11)/(1 - 9*t + 44*t^11 - 36*t^12). (End)

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 14 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 36, -8}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 14 2020 *)

Prog

(Sage)
def A166368_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12) ).list()
A166368_list(30) # G. C. Greubel, Mar 14 2020
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-9*x+44*x^16-36*x^17) )); // G. C. Greubel, Jul 23 2024

Crossrefs

Cf. A003952, A154638, A169452.

Sequence in context: A164779 A165219 A165788 * A166543 A166933 A167111

Adjacent sequences: A166365 A166366 A166367 * A166369 A166370 A166371

Keyword

nonn

Author

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

Status

approved