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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

Table of n, a(n) for n=0..32.

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[0] = a[1] = 1; a[2] = 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.)