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A052541
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Expansion of 1/(1-3x-x^3).
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4
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1, 3, 9, 28, 87, 270, 838, 2601, 8073, 25057, 77772, 241389, 749224, 2325444, 7217721, 22402387, 69532605, 215815536, 669848995, 2079079590, 6453054306, 20029011913, 62166115329, 192951400293, 598883212792, 1858815753705, 5769398661408, 17907079197016
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A transform of A000244 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)). - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 475
Index to sequences with linear recurrences with constant coefficients, signature (3,0,1).
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FORMULA
| G.f.: -1/(-1+3*x+x^3)
Recurrence: {a(0)=1, a(1)=3, a(n)+3*a(n+2)-a(n+3)=0, a(2)=9}
Sum(1/15*(4+_alpha+2*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(-1+3*_Z+_Z^3))
a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)3^(n-3k)}. - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
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MAPLE
| spec := [S, {S=Sequence(Union(Z, Z, Z, Prod(Z, Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| CoefficientList[Series[x/(1 - 3*x - x^3), {x, 0, 60}], x] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 29 2007
LinearRecurrence[{3, 0, 1}, {1, 3, 9}, 50] (* From Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)
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CROSSREFS
| Cf. A076264.
Sequence in context: A005354 A084084 A091140 * A024738 A052939 A085839
Adjacent sequences: A052538 A052539 A052540 * A052542 A052543 A052544
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000
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