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 A163215 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1
 1, 32, 992, 30752, 952816, 29521920, 914703360, 28341043200, 878114994960, 27207394552800, 842990180666400, 26119092121336800, 809270367424023600, 25074322053313752000, 776899354951763496000, 24071343043338616536000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170751, 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..665 Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, -465). FORMULA G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^4 - 30*t^3 - 30*t^2 - 30*t + 1). From G. C. Greubel, Apr 28 2019: (Start) a(n) = 30*(a(n-1) + a(n-2) + a(n-3)) - 465*a(n-4). G.f.: (1+x)*(1-x^4)/(1 - 31*x + 495*x^4 - 465*x^5). (End) MATHEMATICA CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(465*t^4-30*t^3-30*t^2 - 30*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{30, 30, 30, -465}, {1, 32, 992, 30752, 952816}, 20] (* G. C. Greubel, Dec 10 2016 *) PROG (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019 (Magma) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5) )); // G. C. Greubel, Apr 28 2019 (Sage) ((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019 (GAP) a:=[32, 992, 30752, 952816];; for n in [5..20] do a[n]:=30*(a[n-1]+a[n-2] +a[n-3]) -465*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019 CROSSREFS Sequence in context: A264344 A228983 A162836 * A163565 A164036 A164668 Adjacent sequences: A163212 A163213 A163214 * A163216 A163217 A163218 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified September 12 03:03 EDT 2024. Contains 375842 sequences. (Running on oeis4.)