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A052951
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Expansion of (1+x-2x^2)/(1-2x)^2.
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4
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1, 5, 14, 36, 88, 208, 480, 1088, 2432, 5376, 11776, 25600, 55296, 118784, 253952, 540672, 1146880, 2424832, 5111808, 10747904, 22544384, 47185920, 98566144, 205520896, 427819008, 889192448, 1845493760, 3825205248, 7918845952
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OFFSET
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0,2
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COMMENTS
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Equals binomial transform of A042948 starting with "1": (1, 4, 5, 8, 9, 12, 13,...) = terms >0, == 0 or 1 mod 4. [From Gary W. Adamson, Feb 07 2009]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1021
Index to sequences with linear recurrences with constant coefficients, signature (4,-4).
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FORMULA
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G.f.: -(-x+2*x^2-1)/(-1+2*x)^2
Recurrence: {a(0)=1, 4*a(n)-4*a(n+1)+a(n+2)=0, a(1)=5, a(2)=14}
2^n*n+2^n+2^(n-1), n>0.
a(n) = A118413(n+1,n-1) for n>2. - Reinhard Zumkeller, Apr 27 2006
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MAPLE
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spec := [S, {S=Prod(Union(Sequence(Union(Z, Z)), Z), Sequence(Union(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[-(-x+2*x^2-1)/(-1+2*x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 22 2012 *)
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PROG
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(MAGMA) I:=[1, 5, 14]; [n le 3 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 22 2012
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CROSSREFS
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A042948 [From Gary W. Adamson, Feb 07 2009]
Sequence in context: A193557 A187198 A097507 * A048745 A224716 A127980
Adjacent sequences: A052948 A052949 A052950 * A052952 A052953 A052954
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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 08 2000
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STATUS
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approved
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