A169160 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = 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, 201326589, 402653172, 805306335, 1610612652, 3221225268

Offset

0,2

Comments

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

First disagreement at index 27: a(27) = 201326589 , A003945(27) = 201326592. - Klaus Brockhaus, May 07 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 (2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1).

Formula

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

Mathematica

With[{num=Total[t^Range[0, 26]], den=Total[-2*t^Range[1, 25, 2]]+Total[ t^Range[0, 24, 2]]+ t^26}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* Harvey P. Dale, Oct 12 2014 *)

Crossrefs

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

Sequence in context: A169016 A169064 A169112 * A169208 A169256 A169304

Adjacent sequences: A169157 A169158 A169159 * A169161 A169162 A169163

Keyword

nonn

Author

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

Status

approved