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1, 5, 14, 32, 68, 140, 284, 572, 1148, 2300, 4604, 9212, 18428, 36860, 73724, 147452, 294908, 589820, 1179644, 2359292, 4718588, 9437180, 18874364, 37748732, 75497468, 150994940, 301989884, 603979772, 1207959548, 2415919100
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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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a(0) = 1, a(1) = 5, a(n+1) = 2*a(n) + 4, for n >= 1.
a(n) = 9*2^(n-1) - 4, n >= 1.
a(n) = 4*n + Sum[i = 0, n - 1] a(i). - Jon Perry, Nov 20 2012
a(n) = 3*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=5, a(2)=14. - Philippe Deléham, Apr 15 2013
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MATHEMATICA
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Join[{1}, LinearRecurrence[{3, -2}, {5, 14}, 50]] (* G. C. Greubel, Sep 03 2018 *)
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PROG
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(PARI) m=30; v=concat([5, 14], vector(m-2)); for(n=3, m, v[n] = 3*v[n-1] -2*v[n-2]); concat([1], v) \\ G. C. Greubel, Sep 03 2018
(Magma) I:=[5, 14]; [1] cat [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Sep 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)^2)/((1-x)*(1-2*x))); // Marius A. Burtea, Oct 15 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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STATUS
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approved
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