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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

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

Mathematica

Join[{1}, LinearRecurrence[{3, -2}, {5, 14}, 50]] (* G. C. Greubel, Sep 03 2018 *)

Prog

(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

Crossrefs

Cf. A051598, A053208.

Cf. A083329, A131051.

Cf. A048491.

Sequence in context: A139754 A036595 A180668 * A306192 A271993 A274324

Adjacent sequences: A053206 A053207 A053208 * A053210 A053211 A053212

Keyword

nonn,easy

Author

Asher Auel, Dec 14 1999

Status

approved