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A130781
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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.
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4
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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; internal format)
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OFFSET
| 0,3
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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 (paoloplava(AT)gmail.com), Jun 09 2008
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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
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CROSSREFS
| See A130750, A130752, A130755, A129339.
Essentially a duplicate of A024493.
Sequence in context: A091357 A129715 A024493 * A071015 A084188 A044432
Adjacent sequences: A130778 A130779 A130780 * A130782 A130783 A130784
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KEYWORD
| nonn
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jul 14 2007, Jul 18 2007
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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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