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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)