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, 962072674304, 3848290697216, 7696581394432

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,8).

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)

From Amiram Eldar, Feb 19 2026: (Start)

Sum_{n>=0} 1/a(n) = 12/49.

Sum_{n>=0} (-1)^n/a(n) = 4/49. (End)

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 *)

Prog

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

Crossrefs

Cf. A094014, A135530.

Sequence in context: A237686 A170918 A033650 * A241201 A295388 A020700

Adjacent sequences: A135533 A135534 A135535 * A135537 A135538 A135539

Keyword

nonn,easy

Author

Paul Curtz, Feb 22 2008

Extensions

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

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

Status

approved