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A170252
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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)^41 = I.
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0
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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
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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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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, 2, -1, 2, -1, 2, -1).
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FORMULA
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G.f. (t^40 + t^39 + t^38 + t^37 + t^36 + t^35 + 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^40 - 2*t^39 +
t^38 - 2*t^37 + t^36 - 2*t^35 + 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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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