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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

%I

%S 1,1,2,5,11,22,43,85,170,341,683,1366,2731,5461,10922,21845,43691,

%T 87382,174763,349525,699050,1398101,2796203,5592406,11184811,22369621,

%U 44739242,89478485,178956971,357913942,715827883,1431655765,2863311530

%N 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.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 2).

%F 3a(n)=2^(n+1) + periodic {1 -1 -2 -1 1 2}.

%F Also first differences of A024494.

%F G.f.: (1-2x+2x^2)/(1-3x+3x^2-2x^3).

%F 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.]

%F 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

%t a[n_] := a[n] = 3 a[n - 1] - 3 a[n - 2] + 2 a[n - 3]; a[0] = a[1] = 1; a[2] = 2; Table[a@n, {n, 0, 33}] (* Or *) - _Robert G. Wilson v_, Sep 08 2007

%t 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

%t LinearRecurrence[{3,-3,2},{1,1,2},40] (* _Harvey P. Dale_, Sep 17 2013 *)

%Y See A130750, A130752, A130755, A129339.

%Y Essentially a duplicate of A024493.

%K nonn

%O 0,3

%A _Paul Curtz_, Jul 14 2007, Jul 18 2007

%E Edited by _N. J. A. Sloane_, Jul 28 2007

%E More terms from _Robert G. Wilson v_, Sep 08 2007

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Last modified May 14 04:27 EDT 2021. Contains 343872 sequences. (Running on oeis4.)