%I #36 Oct 27 2023 22:00:45

%S 1,5,14,32,68,140,284,572,1148,2300,4604,9212,18428,36860,73724,

%T 147452,294908,589820,1179644,2359292,4718588,9437180,18874364,

%U 37748732,75497468,150994940,301989884,603979772,1207959548,2415919100

%N Row sums of A051598.

%H G. C. Greubel, <a href="/A053209/b053209.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F a(0) = 1, a(1) = 5, a(n+1) = 2*a(n) + 4, for n >= 1.

%F a(n) = 9*2^(n-1) - 4, n >= 1.

%F a(n) = 4*n + Sum[i = 0, n - 1] a(i). - _Jon Perry_, Nov 20 2012

%F a(n) = A048491(n)/2, n>0. - _Philippe Deléham_, Apr 15 2013

%F G.f.: (1+x)^2/((1-x)*(1-2*x)). - _Philippe Deléham_, Apr 15 2013

%F 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

%F E.g.f.: (1 - 8*exp(x) + 9*exp(2*x))/2. - _Stefano Spezia_, Sep 28 2022

%t Join[{1}, LinearRecurrence[{3, -2}, {5, 14}, 50]] (* _G. C. Greubel_, Sep 03 2018 *)

%o (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

%o (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

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)^2)/((1-x)*(1-2*x))); // _Marius A. Burtea_, Oct 15 2019

%Y Cf. A051598, A053208.

%Y Cf. A083329, A131051.

%Y Cf. A048491.

%K nonn,easy

%O 0,2

%A _Asher Auel_, Dec 14 1999