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A169544
Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = 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
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, 2, -1).
FORMULA
G.f. (t^34 + t^33 + 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^34 - 2*t^33 + 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[34]]+1, den=Total[t^Range[2, 34, 2]]+Total[-2 t^Range[1, 33, 2]]+ 1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* Harvey P. Dale, May 15 2014 *)
CROSSREFS
Sequence in context: A169400 A169448 A169496 * A170012 A170060 A170108
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved