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A052531
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If n is even then 2^n+1 otherwise 2^n.
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1
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2, 2, 5, 8, 17, 32, 65, 128, 257, 512, 1025, 2048, 4097, 8192, 16385, 32768, 65537, 131072, 262145, 524288, 1048577, 2097152, 4194305, 8388608, 16777217, 33554432, 67108865, 134217728, 268435457, 536870912, 1073741825, 2147483648
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 461
Index to sequences with linear recurrences with constant coefficients, signature (2,1,-2).
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FORMULA
| G.f.: ( 2-2*x-x^2 ) / ( (x-1)*(2*x-1)*(1+x) ).
Recurrence: {a(1)=2, a(2)=5, a(0)=2, -2*a(n)-a(n+1)+a(n+2)+1=0.}
2^n+Sum(1/2*_alpha^(-n), _alpha=RootOf(-1+_Z^2))
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MAPLE
| spec := [S, {S=Union(Sequence(Union(Z, Z)), Sequence(Prod(Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| 2^# + (1 - Mod[ #, 2]) & /@ Range[0, 31] - from Peter Pein
f1[n_]:=2*n+1; f2[n_]:=2*(n-1); a=2; 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
| Sequence in context: A006367 A077902 A005834 * A095005 A019086 A076949
Adjacent sequences: A052528 A052529 A052530 * A052532 A052533 A052534
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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
Better definition from Peter Pein (petsie(AT)dordos.net), Jan 11 2008
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