A053209 Row sums of A051598.
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
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-2).
Programs
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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
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Magma
R
:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)^2)/((1-x)*(1-2*x))); // Marius A. Burtea, Oct 15 2019 -
Mathematica
Join[{1}, LinearRecurrence[{3, -2}, {5, 14}, 50]] (* G. C. Greubel, Sep 03 2018 *) -
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
Formula
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) = A048491(n)/2, n>0. - Philippe Deléham, Apr 15 2013
G.f.: (1+x)^2/((1-x)*(1-2*x)). - Philippe Deléham, Apr 15 2013
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
E.g.f.: (1 - 8*exp(x) + 9*exp(2*x))/2. - Stefano Spezia, Sep 28 2022