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 A135446 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3). 1
 -1, -1, 3, 10, 19, 33, 62, 125, 255, 514, 1027, 2049, 4094, 8189, 16383, 32770, 65539, 131073, 262142, 524285, 1048575, 2097154, 4194307, 8388609, 16777214, 33554429, 67108863, 134217730, 268435459, 536870913, 1073741822 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence identical to its third differences. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3, -3, 2). FORMULA a(n+1) - 2*a(n) = hexaperiodic 1, 5, 4, -1, -5, -4, A130815. a(n) = 2^n - 2*cos((Pi*n)/3) - (4*sqrt(3)/3)*sin((Pi*n)/3). Or, a(n) = 2^n + [ -2; -3; -1; 2; 3; 1]. - Richard Choulet, Dec 31 2007 G.f.: (1+x)*(1-3*x) / ( (2*x-1)*(x^2-x+1) ). - R. J. Mathar, Nov 07 2015 MATHEMATICA a = {-1, -1, 3}; Do[AppendTo[a, 3*a[[ -1]] - 3*a[[ -2]] + 2*a[[ -3]]], {40}]; a (* Stefan Steinerberger, Dec 22 2007 *) LinearRecurrence[{3, -3, 2}, {-1, -1, 3}, 31] (* Ray Chandler, Sep 23 2015 *) CROSSREFS Sequence in context: A028878 A010896 A234940 * A160002 A294421 A027177 Adjacent sequences: A135443 A135444 A135445 * A135447 A135448 A135449 KEYWORD sign,easy AUTHOR Paul Curtz, Dec 13 2007 STATUS approved

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Last modified May 21 08:56 EDT 2024. Contains 372733 sequences. (Running on oeis4.)