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A170701
Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170739, 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 190. - Vincenzo Librandi, Dec 08 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
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)/(171*t^50 - 18*t^49 - 18*t^48 - 18*t^47 - 18*t^46 - 18*t^45 -
18*t^44 - 18*t^43 - 18*t^42 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 -
18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 -
18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 -
18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 -
18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 -
18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 -
18*t + 1)
MATHEMATICA
With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-18 t^Range[49]] + 171t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 2012 *)
CROSSREFS
Sequence in context: A170557 A170605 A170653 * A170739 A218722 A358109
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved