login
A135098
Duplicate of A136488.
3
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
0,2
COMMENTS
Previous name was: First differences of A135094.
Apart to offset same as A136488.
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
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 *)
PROG
(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
CROSSREFS
Cf. A135094, A136488 (same up to offset).
Sequence in context: A093370 A372957 A094537 * A136488 A045621 A026655
KEYWORD
dead
AUTHOR
Paul Curtz, Feb 12 2008
EXTENSIONS
More terms from R. J. Mathar, Feb 15 2008
STATUS
approved