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A167697
Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.
1
1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222656250, 61988830566406250, 1549720764160156250, 38743019104003906250, 968575477600097655925
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170745, 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 (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).
FORMULA
G.f.: (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)/(300*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
MATHEMATICA
coxG[{15, 300, -24}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 15 2015 *)
CoefficientList[Series[(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)/(300*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 20 2016 *)
CROSSREFS
Sequence in context: A166613 A167079 A167225 * A167941 A168703 A168751
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved