A169208 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653181, 805306356, 1610612703, 3221225388

Offset

0,2

Comments

The initial terms coincide with those of A003945, although the two sequences are eventually different.

First disagreement at index 28: a(28) = 402653181, A003945(28) = 402653184. - Klaus Brockhaus, May 24 2011

Computed with Magma using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1).

Formula

G.f.: (t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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)/(t^28 - t^27 - t^26 - t^25 - t^24 - t^23 - t^22 - t^21 - t^20 - t^19 - t^18 - t^17 - t^16 - t^15 - t^14 - t^13 - t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1).

Mathematica

With[{num=Total[2t^Range[27]]+t^28+1, den=Total[-t^Range[27]]+t^28+1}, CoefficientList[ Series[num/den, {t, 0, 35}], t]] (* Harvey P. Dale, Sep 09 2011 *)

Crossrefs

Cf. A003945 (G.f.: (1+x)/(1-2*x)).

Sequence in context: A169112 A169160 A122391 * A169256 A169304 A169352

Adjacent sequences: A169205 A169206 A169207 * A169209 A169210 A169211

Keyword

nonn

Author

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

Status

approved