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A052950
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Expansion of (2-3x-x^2+x^3)/((1-x)(1+x)(1-2x)).
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3
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2, 1, 3, 4, 9, 16, 33, 64, 129, 256, 513, 1024, 2049, 4096, 8193, 16384, 32769, 65536, 131073, 262144, 524289, 1048576, 2097153, 4194304, 8388609, 16777216, 33554433, 67108864, 134217729, 268435456, 536870913, 1073741824, 2147483649
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Equals row sums of triangle A178616 but replacing the 2 with a 1. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2010]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1009
Index to sequences with linear recurrences with constant coefficients, signature (2,1,-2).
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FORMULA
| G.f.: (x^3-x^2-3*x+2)/(-1+2*x)/(-1+x^2)
Recurrence: {a(1)=1, a(3)=4, a(2)=3, a(0)=2, -2*a(n)-a(n+1)+a(n+2)+1=0}
2^(n-1)+Sum(1/2*_alpha^(-n), _alpha=RootOf(-1+_Z^2))
E.g.f. : cosh(x)(1+exp(x)); a(n)=(2^n+1+(-1)^n+0^n)/2. - Paul Barry (pbarry(AT)wit.ie), Sep 18 2003
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MAPLE
| spec := [S, {S=Union(Sequence(Prod(Sequence(Z), Z)), Sequence(Prod(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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MATHEMATICA
| f1[n_]:=2*n+1; f2[n_]:=2*(n-1); a=1; lst={a}; Do[AppendTo[lst, a=f1[a]]; AppendTo[lst, a=f2[a]], {n, 20}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 07 2010]
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CROSSREFS
| A178616 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2010]
Sequence in context: A019612 A007444 A166476 * A086851 A001054 A141487
Adjacent sequences: A052947 A052948 A052949 * A052951 A052952 A052953
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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 05 2000
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