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 A162785 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I. 2
 1, 15, 210, 2835, 38220, 514605, 6928740, 93285465, 1255955610, 16909618635, 227663487870, 3065158424055, 41267909559240, 555612506386665, 7480515990707760, 100714290692336685, 1355971748798391270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170734, although the two sequences are eventually different. Computed with MAGMA using commands similar to those used to compute A154638. LINKS G. C. Greubel, Table of n, a(n) for n = 0..880 Index entries for linear recurrences with constant coefficients, signature (13, 13, -91). FORMULA G.f.: (t^3 + 2*t^2 + 2*t + 1)/(91*t^3 - 13*t^2 - 13*t + 1). G.f.: (1+x)*(1-x^3)/(1 - 14*x + 104*x^3 - 91*x^4). - G. C. Greubel, Apr 26 2019 MATHEMATICA CoefficientList[Series[(1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4), {x, 0, 20}], x] (* or *) coxG[{3, 91, -13}] (* 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^3)/(1-14*x+104*x^3-91*x^4)) \\ G. C. Greubel, Apr 26 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4) )); // G. C. Greubel, Apr 26 2019 (Sage) ((1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019 (GAP) a:=[15, 210, 2835];; for n in [4..20] do a[n]:=13*a[n-1]+13*a[n-2] -91*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 26 2019 CROSSREFS Sequence in context: A234249 A112496 A000483 * A076139 A163091 A163440 Adjacent sequences:  A162782 A162783 A162784 * A162786 A162787 A162788 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)