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A168729
Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
1
1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131876, 57395628, 172186884, 516560646, 1549681920, 4649045712, 13947136992, 41841410544, 125524230336, 376572687120, 1129718049696
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003946, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 516560646, A003946(18) = 516560652. - Klaus Brockhaus, Mar 27 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).
FORMULA
G.f.: (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)/(3*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).
MATHEMATICA
CoefficientList[Series[(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)/(3*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), {t, 0, 50}], t] (* G. C. Greubel, Aug 06 2016 *)
coxG[{18, 3, -2, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 07 2016 *)
CROSSREFS
Cf. A003946 (G.f.: (1+x)/(1-3*x)).
Sequence in context: A167649 A167882 A168681 * A168777 A168825 A168873
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved