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A170708
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Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
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1
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1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
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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 A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
About the initial comment, first disagreement is at index 50 and the difference is 351. - Vincenzo Librandi, Dec 06 2012]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
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FORMULA
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G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + ,2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + ,2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + ,2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + ,2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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)/(325*t^50 - 25*t^49 - 25*t^48 - 25*t^47 - 25*t^46 - 25*t^45 - ,25*t^44 - 25*t^43 - 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - ,25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - ,25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - ,25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - ,25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - ,25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - ,25*t + 1).
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MATHEMATICA
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With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-25 t^Range[49]] + 325 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Vincenzo Librandi, Dec 06 2012 *)
coxG[{50, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 07 2019 *)
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CROSSREFS
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Sequence in context: A170564 A170612 A170660 * A170746 A218729 A171332
Adjacent sequences: A170705 A170706 A170707 * A170709 A170710 A170711
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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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