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A170704
Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460544, 295665060514131968, 6504631331310903296, 143101889288839872512
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170742, 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 253. - Vincenzo Librandi, Dec 08 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
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)/(231*t^50 - 21*t^49 - 21*t^48 - 21*t^47 - 21*t^46 - 21*t^45 -
21*t^44 - 21*t^43 - 21*t^42 - 21*t^41 - 21*t^40 - 21*t^39 - 21*t^38 -
21*t^37 - 21*t^36 - 21*t^35 - 21*t^34 - 21*t^33 - 21*t^32 - 21*t^31 -
21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 -
21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 -
21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 -
21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 -
21*t + 1)
MATHEMATICA
With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-21 t^Range[49]] + 231t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 2012 *)
coxG[{50, 231, -21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 10 2017 *)
CROSSREFS
Sequence in context: A170560 A170608 A170656 * A170742 A218725 A136285
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved