A166558 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818866, 115909305825456, 1390911669894318, 16690940038597968, 200291280461569440, 2403495365519559168, 28841944386003420672, 346103332629265575936

Offset

0,2

Comments

The initial terms coincide with those of A170732, 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 (11,11,11,11,11,11,11,11,11,11,11,-66).

Formula

G.f.: (t^12 + 2*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)/(66*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t +1).

From G. C. Greubel, Dec 03 2024: (Start)

a(n) = 11*Sum_{j=1..11} a(n-j) - 66*a(n-12).

G.f.: (1+x)*(1-x^12)/(1 - 12*x + 77*x^12 - 66*x^13). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^12)/(1-12*t+77*t^12-66*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 17 2016; Dec 03 2024 *)
coxG[{12, 66, -11}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 03 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x)*(1-x^12)/(1-12*x+77*x^12-66*x^13) )); // G. C. Greubel, Dec 03 2024
(SageMath)
def A166558_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-12*x+77*x^12-66*x^13) ).list()
A166558_list(40) # G. C. Greubel, Dec 03 2024

Crossrefs

Cf. A154638, A169452, A170732.

Sequence in context: A165269 A165873 A166377 * A166954 A167114 A167669

Adjacent sequences: A166555 A166556 A166557 * A166559 A166560 A166561

Keyword

nonn

Author

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

Status

approved