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 A130781 Sequence is identical to its third differences: a(n+3)=3a(n+2)-3a(n+1)+2a(n), with a(0)=a(1)=1, a(2)=2. 6
 1, 1, 2, 5, 11, 22, 43, 85, 170, 341, 683, 1366, 2731, 5461, 10922, 21845, 43691, 87382, 174763, 349525, 699050, 1398101, 2796203, 5592406, 11184811, 22369621, 44739242, 89478485, 178956971, 357913942, 715827883, 1431655765, 2863311530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Index entries for linear recurrences with constant coefficients, signature (3, -3, 2). FORMULA 3a(n)=2^(n+1) + periodic {1 -1 -2 -1 1 2}. Also first differences of A024494. G.f.: (1-2x+2x^2)/(1-3x+3x^2-2x^3). Binomial transform of [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,...]; i.e. ones in positions 2, 5, 8, 11,... and the rest zeros. [Corrected by Gary W. Adamson, Jan 07 2008.] a(n)=(1/6)*{1/2-(1/2)*I*sqrt(3)}^n+(1/6)*{1/2+(1/2)*I*sqrt(3)}^n+(2/3)*2^n-(1/6)*I*{1/2-(1 /2)*I*sqrt(3)}^n*sqrt(3)+(1/6)*I*{1/2+(1/2)*I*sqrt(3)}^n*sqrt(3), with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jun 09 2008 MATHEMATICA a[n_] := a[n] = 3 a[n - 1] - 3 a[n - 2] + 2 a[n - 3]; a = a = 1; a = 2; Table[a@n, {n, 0, 33}] (* Or *) - Robert G. Wilson v, Sep 08 2007 CoefficientList[ Series[(1 - 2 x + 2 x^2)/(1 - 3 x + 3 x^2 - 2 x^3), {x, 0, 33}], x] - Robert G. Wilson v, Sep 08 2007 LinearRecurrence[{3, -3, 2}, {1, 1, 2}, 40] (* Harvey P. Dale, Sep 17 2013 *) CROSSREFS See A130750, A130752, A130755, A129339. Essentially a duplicate of A024493. Sequence in context: A309950 A129715 A024493 * A071015 A293362 A084188 Adjacent sequences:  A130778 A130779 A130780 * A130782 A130783 A130784 KEYWORD nonn AUTHOR Paul Curtz, Jul 14 2007, Jul 18 2007 EXTENSIONS Edited by N. J. A. Sloane, Jul 28 2007 More terms from Robert G. Wilson v, Sep 08 2007 STATUS approved

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Last modified April 17 14:32 EDT 2021. Contains 343063 sequences. (Running on oeis4.)