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A052931
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Expansion of 1/(1-3x^2-x^3).
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8
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1, 0, 3, 1, 9, 6, 28, 27, 90, 109, 297, 417, 1000, 1548, 3417, 5644, 11799, 20349, 41041, 72846, 143472, 259579, 503262, 922209, 1769365, 3269889, 6230304, 11579032, 21960801, 40967400, 77461435, 144863001, 273351705, 512050438, 964918116, 1809503019
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let A be the tridiagonal unit-primitive matrix (see [Jeffery]) A = A_{9,1} = [0,1,0,0; 1,0,1,0; 0,1,0,1; 0,0,1,1]. Then a(n)=[A^n]_(2,3). - L. Edson Jeffery, Mar 19 2011
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 917
Index to sequences with linear recurrences with constant coefficients, signature (0,3,1)
L. E. Jeffery, Unit-primitive matrices
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FORMULA
| G.f.: -1/(-1+3*x^2+x^3)
Recurrence: {a(1)=0, a(0)=1, a(2)=3, a(n)+3*a(n+1)-a(n+3)=0.}
Sum(1/9*(-1+5*_alpha+2*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(-1+3*_Z^2+_Z^3))
a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)3^(3k-n)} - Paul Barry (pbarry(AT)wit.ie), Oct 04 2004
a(n)=A187497(3*(n+1)). - L. Edson Jeffery, Mar 19 2011.
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MAPLE
| spec := [S, {S=Sequence(Prod(Z, Union(Z, Z, Z, Prod(Z, Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| CoefficientList[Series[1/(1-3x^2-x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 3, 1}, {1, 0, 3}, 40] (* From Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)
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CROSSREFS
| Sequence in context: A157393 A127552 A185580 * A006803 A197730 A143495
Adjacent sequences: A052928 A052929 A052930 * A052932 A052933 A052934
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KEYWORD
| easy,nonn,changed
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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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