A164120 Partial sums of A162396.

5, 7, 17, 21, 41, 49, 89, 105, 185, 217, 377, 441, 761, 889, 1529, 1785, 3065, 3577, 6137, 7161, 12281, 14329, 24569, 28665, 49145, 57337, 98297, 114681, 196601, 229369, 393209, 458745, 786425, 917497, 1572857, 1835001, 3145721, 3670009

Offset: 1

Author

Klaus Brockhaus, Aug 10 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2).

Crossrefs

Cf. A162396, A164053 (partial sums of A162255).

Programs

Magma

T:=[ n le 2 select 8-3*n else 2*Self(n-2): n in [1..38] ]; [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T]];

Mathematica

Rest[CoefficientList[Series[x*(5 + 2*x)/((1 - x)*(1 - 2*x^2)), {x,0,50}], x]] (* or *) LinearRecurrence[{1,2,-2}, {5,7,17}, 50] (* G. C. Greubel, Sep 12 2017 *)

PARI

x='x+O('x^50); Vec(x*(5+2*x)/((1-x)*(1-2*x^2))) \\ G. C. Greubel, Sep 12 2017

Formula

a(n) = 2*a(n-2) + 7 for n > 2; a(1) = 5, a(2) = 7.

a(n) = (19 - 5*(-1)^n)*2^((2*n-1+(-1)^n)/4)/2 - 7.

G.f.: x*(5+2*x)/((1-x)*(1-2*x^2)).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3). - G. C. Greubel, Sep 12 2017