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 A163924 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
 1, 8, 56, 392, 2744, 19208, 134428, 940800, 6584256, 46080384, 322496832, 2257016832, 15795891636, 110548662840, 773682621768, 5414672451384, 37894967433288, 265210605012024, 1856095143363468, 12990012903371952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A003950, 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 (6,6,6,6,6,-21). FORMULA G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1). a(n) = -21*a(n-6) + 6*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021 MAPLE seq(coeff(series((1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019 MATHEMATICA coxG[{6, 21, -6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 24 2016 *) CoefficientList[Series[(1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 08 2017 *) PROG (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7)) \\ G. C. Greubel, Aug 08 2017 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7) )); // G. C. Greubel, Aug 10 2019 (Sage) def A163924_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7)).list() A163924_list(30) # G. C. Greubel, Aug 10 2019 (GAP) a:=[8, 56, 392, 2744, 19208, 134428];; for n in [7..30] do a[n]:=6*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -21*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019 CROSSREFS Sequence in context: A063812 A234274 A163347 * A164373 A164769 A165215 Adjacent sequences: A163921 A163922 A163923 * A163925 A163926 A163927 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified October 3 09:00 EDT 2023. Contains 365854 sequences. (Running on oeis4.)