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A170722
Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170760, 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 820. - Vincenzo Librandi, Dec 06 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
FORMULA
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)/(780*t^50 - 39*t^49 - 39*t^48 - 39*t^47 - 39*t^46 - 39*t^45 -
39*t^44 - 39*t^43 - 39*t^42 - 39*t^41 - 39*t^40 - 39*t^39 - 39*t^38 -
39*t^37 - 39*t^36 - 39*t^35 - 39*t^34 - 39*t^33 - 39*t^32 - 39*t^31 -
39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 - 39*t^24 -
39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 -
39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 -
39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 -
39*t + 1)
MATHEMATICA
With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-39 t^Range[49]] + 780 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Vincenzo Librandi, Dec 06 2012 *)
CROSSREFS
Sequence in context: A170578 A170626 A170674 * A170760 A167957 A218743
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved