A169448 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = 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, 402653184, 805306368, 1610612736, 3221225472

Offset

0,2

Comments

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

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, 2, -1, 2, -1, 2, -1).

Formula

G.f. (t^32 + t^31 + t^30 + t^29 + 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)/(t^32 - 2*t^31 + t^30 - 2*t^29 + t^28 - 2*t^27 + 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[32]]+1, den=Total[-2 t^Range[1, 31, 2]] + Total[ t^Range[2, 32, 2]]+1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* Harvey P. Dale, Aug 10 2012 *)

Crossrefs

Sequence in context: A169304 A169352 A169400 * A169496 A169544 A170012

Adjacent sequences: A169445 A169446 A169447 * A169449 A169450 A169451

Keyword

nonn

Author

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

Status

approved