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A165979
Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
2
1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332001, 3811511582622900, 99099301147958475, 2576581829840760300, 66991127575699606500, 1741769316964025575200
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170746, 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 (25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
FORMULA
G.f.: (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)/(325*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
G.f.: (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11). - G. C. Greubel, Apr 26 2019
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11), {x, 0, 20}], x] (* G. C. Greubel, Apr 20 2016, modified Apr 26 2019 *)
coxG[{10, 325, -25}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
CROSSREFS
Sequence in context: A164644 A164969 A165445 * A166421 A166614 A167080
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved