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A168776
Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
1
1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786429, 1572852, 3145695, 6291372, 12582708, 25165344, 50330544, 100660800, 201321024, 402640896, 805279488, 1610554368, 3221099520
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003945, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 786429, A003945(19) = 786432.
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).
FORMULA
G.f.: (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^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
CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, Aug 12 2016 *)
CROSSREFS
Cf. A003945 (G.f.: (1+x)/(1-2*x)).
Sequence in context: A167881 A168680 A168728 * A168824 A168872 A168920
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved