A135536 a(n) = 8*a(n-2), with a(0) = 7, a(1) = 14.

7, 14, 56, 112, 448, 896, 3584, 7168, 28672, 57344, 229376, 458752, 1835008, 3670016, 14680064, 29360128, 117440512, 234881024, 939524096, 1879048192, 7516192768, 15032385536, 60129542144, 120259084288, 481036337152

Offset: 0

Author

Paul Curtz, Feb 22 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,8).

Programs

Mathematica

Table[(7/4)*( (2 + Sqrt[2]) + (-1)^n*(2 - Sqrt[2]) )*(Sqrt[2])^(3*n), {n,0,25}] (* or *) LinearRecurrence[{0,8},{7,14}, 25] (* G. C. Greubel, Oct 18 2016 *)

PARI

a(n)=([0,1; 8,0]^n*[7;14])[1,1] \\ Charles R Greathouse IV, Oct 18 2016

Formula

a(n) = b(3*n) + b(3*n + 1) + b(3*n + 2), where b(n) = A135530(n) [previous name].

a(n) = 7 * abs(A094014(n)).

O.g.f.: 7*(1 + 2*x)/(1 - 8*x^2). - R. J. Mathar, Feb 23 2008

From G. C. Greubel, Oct 18 2016: (Start)

a(n) = (7/4)*( (2 + sqrt(2)) + (-1)^n*(2 - sqrt(2)) )*(sqrt(2))^(3*n).

a(n) = 8*a(n-2).

E.g.f.: (7/2)*( 2*cosh(2*sqrt(2)*x) + sqrt(2)*sinh(2*sqrt(2)*x) ). (End)

Extensions

More terms from R. J. Mathar, Feb 23 2008

New name from G. C. Greubel, Oct 18 2016