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A166377
Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
3
1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734834, 9659108817072, 115909305793710, 1390911669390672, 16690940031081888, 200291280353708544
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170732, 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 (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
FORMULA
G.f.: (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)/(66*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
G.f.: (1 + t - t^11 - t^12)/(1 - 12*t + 77*t^11 - 66*t^12). - Zak Seidov, Dec 05 2009
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^11)/(1-12*t+77*t^11-66*t^12), {t, 0, 20}], t] (* G. C. Greubel, May 10 2016 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A164815 A165269 A165873 * A166558 A166954 A167114
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved