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A168808
Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
1
1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170754, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 129029362371099459501507214765, A170754(19) = 129029362371099459501507215360. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).
FORMULA
G.f.: (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)/(561*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
MATHEMATICA
With[{num=Total[2t^Range[18]]+t^19+1, den=Total[-33 t^Range[18]]+ 561t^19+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Mar 11 2012 *)
CROSSREFS
Cf. A170754 (G.f.: (1+x)/(1-34*x)).
Sequence in context: A167951 A168712 A168760 * A168856 A168904 A168952
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved