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A153643
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Jacobsthal numbers A001045 incremented by 2.
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6
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2, 3, 3, 5, 7, 13, 23, 45, 87, 173, 343, 685, 1367, 2733, 5463, 10925, 21847, 43693, 87383, 174765, 349527, 699053, 1398103, 2796205, 5592407, 11184813, 22369623, 44739245, 89478487, 178956973, 357913943, 715827885, 1431655767, 2863311533, 5726623063
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (2 - x - 5*x^2)/((1+x)*(1-x)*(1-2*x)). - R. J. Mathar, Jan 23 2009
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n >= 3. - Andrew Howroyd, Feb 26 2018
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MATHEMATICA
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LinearRecurrence[{1, 2}, {0, 1}, 40] + 2 (* Harvey P. Dale, May 26 2014 *)
LinearRecurrence[{2, 1, -2}, {2, 3, 3}, 40] (* Georg Fischer, Apr 02 2019 *)
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PROG
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(PARI) my(x='x+O('x^40)); Vec( (2-x-5*x^2)/((1-x^2)*(1-2*x)) ) \\ G. C. Greubel, Apr 02 2019
(Magma) I:=[2, 3, 3]; [n le 3 select I[n] else 2*Self(n-1) +Self(n-2) -2*Self(n-3): n in [1..40]]; // G. C. Greubel, Apr 02 2019
(Sage) ((2-x-5*x^2)/((1-x^2)*(1-2*x))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 02 2019
(GAP) a:=[2, 3, 3];; for n in [4..40] do a[n]:=2*a[n-1]+a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Apr 02 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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