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A052947
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Expansion of 1/(1-x^2-2x^3).
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14
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1, 0, 1, 2, 1, 4, 5, 6, 13, 16, 25, 42, 57, 92, 141, 206, 325, 488, 737, 1138, 1713, 2612, 3989, 6038, 9213, 14016, 21289, 32442, 49321, 75020, 114205, 173662, 264245, 402072, 611569, 930562, 1415713, 2153700, 3276837, 4985126, 7584237, 11538800
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..41.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1006
Index to sequences with linear recurrences with constant coefficients, signature (0,1,2).
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FORMULA
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Recurrence: {a(1)=0, a(0)=1, a(2)=1, 2*a(n)+a(n+1)-a(n+3)=0}.
Sum(-1/52*(-3-17*_alpha+2*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(_Z^2+2*_Z^3-1))
a(n) = sum{k=0..floor(n/2), C(k,n-2k)2^(n-2k)}. - Paul Barry, Oct 16 2004
If p[1]=0, p[2]=1, p[3]=2, p[i]=0, (i>3), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=det A. - Milan Janjic, May 02 2010
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Prod(Union(Z, Z), Z), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
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Column k=2 of A219946. - Alois P. Heinz, Dec 01 2012
Sequence in context: A058359 A110332 * A159287 A021992 A080030 A125156
Adjacent sequences: A052944 A052945 A052946 * A052948 A052949 A052950
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers, Jun 05 2000
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STATUS
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approved
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