A135098 Duplicate of A136488.

1, 2, 5, 10, 22, 44, 92, 184, 376, 752, 1520, 3040, 6112, 12224, 24512, 49024, 98176, 196352, 392960, 785920, 1572352, 3144704, 6290432, 12580864, 25163776, 50327552, 100659200, 201318400, 402644992, 805289984, 1610596352, 3221192704

Offset: 0

Author

Paul Curtz, Feb 12 2008

Keywords

• dead

Comments

Previous name was: First differences of A135094.

Apart to offset same as A136488.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,2,-4).

Crossrefs

Cf. A135094, A136488 (same up to offset).

Programs

Mathematica

Table[2^((n - 5)/2)*( 3*2^((n + 1)/2) - (1 - (-1)^n) - (1 + (-1)^n)*Sqrt[2] ), {n, 1, 50}] (* or *) LinearRecurrence[{2, 2, -4}, {1, 2, 5}, 25] (* G. C. Greubel, Sep 23 2016 *)

PARI

a(n)=([0,1,0; 0,0,1; -4,2,2]^n*[1;2;5])[1,1] \\ Charles R Greathouse IV, Sep 23 2016

Formula

From R. J. Mathar, Feb 15 2008: (Start)

O.g.f.: (2*x+1) / (2*(2*x^2-1)) -3 / (2*(2*x-1)).

a(n) = (-A016116(n+1) +A007283(n)) / 2 . (End)

G.f.: (1 - x)*(1 + x) / ((1 - 2*x)*(1 - 2*x^2)). - Arkadiusz Wesolowski, Oct 24 2013

From G. C. Greubel, Sep 23 2016: (Start)

a(n) = 2^((n-4)/2)*( 6*2^(n/2) - (1 + (-1)^n) - (1 - (-1)^n)*sqrt(2) ).

E.g.f.: (1/2)*( 3*exp(2*x) - cosh(sqrt(2)*x) - sqrt(2)*sinh(sqrt(2)*x) ). (End) [corrected by Jason Yuen, Sep 25 2024]

a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3). - Wesley Ivan Hurt, Apr 07 2021

Extensions

More terms from R. J. Mathar, Feb 15 2008