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A052549
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a(n) = 5*2^(n-1) - 1, n>0, with a(0)=1.
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9
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1, 4, 9, 19, 39, 79, 159, 319, 639, 1279, 2559, 5119, 10239, 20479, 40959, 81919, 163839, 327679, 655359, 1310719, 2621439, 5242879, 10485759, 20971519, 41943039, 83886079, 167772159, 335544319, 671088639, 1342177279, 2684354559
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OFFSET
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0,2
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COMMENTS
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Equals binomial transform of [1, 3, 2, 3, 2, 3, 2, ...]. - Gary W. Adamson, May 11 2008
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LINKS
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FORMULA
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G.f.: (1 + x - x^2)/((1-2*x)*(1-x)).
a(n) = 2*a(n-1) + 1, for n>1, with a(0)=1 and a(1)=4.
E.g.f.: (5*exp(2*x) - 2*exp(x) - 1)/2. - G. C. Greubel, May 07 2019
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MAPLE
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spec := [S, {S=Prod(Sequence(Union(Z, Z)), Union(Z, Sequence(Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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LinearRecurrence[{3, -2}, {1, 4, 9}, 30] (* G. C. Greubel, May 07 2019 *)
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PROG
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(PARI) vector(30, n, n--; if(n==0, 1, 5*2^(n-1) -1)) \\ G. C. Greubel, May 07 2019
(Magma) [n eq 0 select 1 else 5*2^(n-1) -1: n in [0..30]]; // G. C. Greubel, May 07 2019
(Sage) [1]+[5*2^(n-1) -1 for n in (1..30)] # G. C. Greubel, May 07 2019
(GAP) Concatenation([1], List([1..30], n-> 5*2^(n-1) -1)) # G. C. Greubel, May 07 2019
(Python)
a052549 = [1] + [(5<<(n-1))-1 for n in range(1, 30)]
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CROSSREFS
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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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