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A052996
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G.f.: (1+x^2-x^3)/((1-x)(1-2*x)).
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12
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1, 3, 8, 17, 35, 71, 143, 287, 575, 1151, 2303, 4607, 9215, 18431, 36863, 73727, 147455, 294911, 589823, 1179647, 2359295, 4718591, 9437183, 18874367, 37748735, 75497471, 150994943, 301989887, 603979775, 1207959551, 2415919103
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OFFSET
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0,2
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LINKS
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FORMULA
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Recurrence: {-2*a(n)+a(n+1)-1=0, a(0)=1, a(1)=3, a(2)=8}.
a(n) = 9*2^(n-2) - 1 for n > 1. - Brad Clardy, Sep 23 2011
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MAPLE
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spec := [S, {S=Prod(Union(Prod(Z, Z), Sequence(Z)), Sequence(Union(Z, Z)))}, unlabeled ]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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a[0] := 1; a[1] := 3; a[2] := 8; a[n_] := 2*a[n - 1] + 1; Table[a[n], {n, 0, 12}] (* L. Edson Jeffery, Dec 18 2014 *)
CoefficientList[ Series[(1 + x^2 - x^3)/((1 - x) (1 - 2 x)), {x, 0, 30}], x] (* Robert G. Wilson v, Jul 29 2015 *
LinearRecurrence[{3, -2}, {1, 3, 8, 17}, 40] (* Harvey P. Dale, Feb 11 2018 *)
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PROG
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(PARI) Vec((1+x^2-x^3)/((1-x)*(1-2*x)) + O(x^50)) \\ Michel Marcus, Jul 30 2015
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CROSSREFS
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Cf. A050524 (primes of this sequence).
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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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STATUS
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approved
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