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A167882
Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
7
1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131876, 57395622, 172186848, 516560496, 1549681344, 4649043600, 13947129504, 41841384624, 125524142208, 376572391632, 1129717069920
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003946, 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 (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).
FORMULA
G.f.: (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^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^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^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, Jun 29 2016 *)
CROSSREFS
Sequence in context: A166858 A167105 A167649 * A168681 A168729 A168777
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved