A166372 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095146, 3423740045880, 37661140496760, 414272545377240, 4556997998191320, 50126977969563000, 551396757549236280

Offset

0,2

Comments

The initial terms coincide with those of A003954, 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 (10,10,10,10,10,10,10,10,10,10,-55).

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)/(55*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

From G. C. Greubel, Dec 06 2024: (Start)

a(n) = 10*Sum_{j=1..10} a(n-j) - 55*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 11*x + 65*x^11 - 55*x^12). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-11*t+65*t^11-55*t^12), {t, 0, 50}], t] (* G. C. Greubel, May 10 2016; Dec 06 2024 *)
coxG[{11, 55, -10, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 06 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^11)/(1-11*x+65*x^11-55*x^12) )); // G. C. Greubel, Dec 06 2024
(SageMath)
def A166372_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-11*x+65*x^11-55*x^12) ).list()
print(A166372_list(40)) # G. C. Greubel, Dec 06 2024

Crossrefs

Cf. A003954, A154638, A169452.

Sequence in context: A164781 A165266 A165807 * A166557 A166951 A167113

Adjacent sequences: A166369 A166370 A166371 * A166373 A166374 A166375

Keyword

nonn

Author

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

Status

approved