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A166857
Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
1
1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12285, 24564, 49119, 98220, 196404, 392736, 785328, 1570368, 3140160, 6279168, 12556032, 25107456, 50205696, 100392966, 200749089, 401424504, 802701687, 1605108786, 3209628504
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).
FORMULA
G.f.: (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^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
CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, May 25 2016 *)
CROSSREFS
Sequence in context: A165745 A166327 A166467 * A364496 A167104 A167648
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved