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A166467
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Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
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1
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1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6141, 12276, 24543, 49068, 98100, 196128, 392112, 783936, 1567296, 3133440, 6264576, 12524544, 25039878, 50061345, 100085880, 200098167, 400049202, 799804248, 1599020400, 3196865040
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1).
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FORMULA
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G.f.: (t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1).
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MATHEMATICA
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CoefficientList[Series[(t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(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, 0, 10}], t] (* G. C. Greubel, May 15 2016 *)
coxG[{12, 1, -1, 40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 15 2020 *)
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CROSSREFS
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Sequence in context: A046944 A165745 A166327 * A166857 A167104 A167648
Adjacent sequences: A166464 A166465 A166466 * A166468 A166469 A166470
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KEYWORD
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nonn
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AUTHOR
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John Cannon and N. J. A. Sloane, Dec 03 2009
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STATUS
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approved
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