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A166618
Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
1
1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155699999999535, 16474670999999972100, 494240129999998744965, 14827203899999949807900
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170750, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
FORMULA
G.f.: (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)/(435*t^12 - 29*t^11 - 29*t^10 - 29*t^9 -29*t^8 -29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t +1).
MATHEMATICA
CoefficientList[Series[(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)/(435*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 19 2016 *)
coxG[{12, 435, -29}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 26 2020 *)
CROSSREFS
Sequence in context: A165547 A166075 A166425 * A167084 A167378 A167756
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved