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A052919
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a(0)=2; a(n)= 1+2*3^(n-1) for n>0.
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7
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2, 3, 7, 19, 55, 163, 487, 1459, 4375, 13123, 39367, 118099, 354295, 1062883, 3188647, 9565939, 28697815, 86093443, 258280327, 774840979, 2324522935, 6973568803, 20920706407, 62762119219, 188286357655, 564859072963
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| It appears that if s(n) is a first order rational sequence of the form s(1)=3, s(n)=(2*s(n-1)+1)/(s(n-1)+2), n>1, then s(n)= a(n)/(a(n)-2).
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 902
Index to sequences with linear recurrences with constant coefficients, signature (4,-3).
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FORMULA
| 1+2*3^(n-1) for n>0 with a(0) = 2.
G.f.: (2-5*x+x^2)/(-1+3*x)/(-1+x)
Recurrence: {a(1)=3, a(2)=7, a(0)=2, -3*a(n)+a(n+1)+2=0}
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MAPLE
| spec := [S, {S=Union(Sequence(Prod(Sequence(Z), Union(Z, Z))), Sequence(Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| Join[{2}, Table[2*(3^n+1)-1, {n, 0, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 14 2011*)
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CROSSREFS
| Sequence in context: A122724 A033844 A037028 * A005807 A167422 A060276
Adjacent sequences: A052916 A052917 A052918 * A052920 A052921 A052922
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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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