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A170696
Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183360
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170734, 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 105. - Vincenzo Librandi, Dec 08 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
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)/(91*t^50 - 13*t^49 - 13*t^48 - 13*t^47 - 13*t^46 - 13*t^45 -
13*t^44 - 13*t^43 - 13*t^42 - 13*t^41 - 13*t^40 - 13*t^39 - 13*t^38 -
13*t^37 - 13*t^36 - 13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 -
13*t^30 - 13*t^29 - 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 -
13*t^23 - 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 -
13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 -
13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 -
13*t + 1).
MATHEMATICA
With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-13 t^Range[49]] + 91 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 2012 *)
CROSSREFS
Sequence in context: A170552 A170600 A170648 * A170734 A186231 A001880
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved