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 A164352 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I. 1
 1, 3, 6, 12, 24, 48, 96, 189, 372, 735, 1452, 2868, 5664, 11184, 22086, 43617, 86136, 170103, 335922, 663384, 1310064, 2587140, 5109132, 10089609, 19925148, 39348555, 77706264, 153455784, 303047352, 598463580, 1181857074, 2333953461 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A003945, 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..1000 Index entries for linear recurrences with constant coefficients, signature (2, -1, 2, -1, 2, -1). FORMULA G.f.: (t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1). a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-a(n-4)+2*a(n-5)-a(n-6). - Wesley Ivan Hurt, May 11 2021 MAPLE seq(coeff(series((1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6)), t, n+1), t, n), n = 0 .. 35); # G. C. Greubel, Aug 24 2019 MATHEMATICA CoefficientList[Series[(1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6)), {t, 0, 35}], t] (* G. C. Greubel, Sep 15 2017 *) PROG (PARI) (t='t+O('t^35)); Vec((1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5 +t^6))) \\ G. C. Greubel, Sep 15 2017 (MAGMA) R:=PowerSeriesRing(Integers(), 35); Coefficients(R!( (1-t^7)/( (1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6)) )); // G. C. Greubel, Aug 24 2019 (Sage) def A164352_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6))).list() A164352_list(35) # G. C. Greubel, Aug 24 2019 (GAP) a:=[3, 6, 12, 24, 48, 96];; for n in [7..35] do a[n]:=2*a[n-1] -a[n-2]+2*a[n-3]-a[n-4]+2*a[n-5]-a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019 CROSSREFS Sequence in context: A163876 A033893 A006851 * A115829 A115805 A164696 Adjacent sequences:  A164349 A164350 A164351 * A164353 A164354 A164355 KEYWORD nonn,changed AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)