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Search: id:A130781
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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. +0
4
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; listen)
OFFSET

0,3

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 (qntmpkt(AT)yahoo.com), 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 (ppl(AT)spl.at), 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 (rgwv(AT)rgwv.com), 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 (rgwv(AT)rgwv.com), Sep 08 2007

CROSSREFS

See A130750, A130752, A130755, A129339.

Essentially a duplicate of A024493.

Sequence in context: A091357 A129715 A024493 this_sequence A071015 A084188 A044432

Adjacent sequences: A130778 A130779 A130780 this_sequence A130782 A130783 A130784

KEYWORD

nonn

AUTHOR

Paul Curtz (bpcrtz(AT)free.fr), Jul 14 2007, Jul 18 2007

EXTENSIONS

Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 28 2007

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 08 2007

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Last modified December 11 12:57 EST 2009. Contains 170656 sequences.


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