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%I #21 Apr 07 2021 05:11:32
%S 1,2,5,10,22,44,92,184,376,752,1520,3040,6112,12224,24512,49024,98176,
%T 196352,392960,785920,1572352,3144704,6290432,12580864,25163776,
%U 50327552,100659200,201318400,402644992,805289984,1610596352,3221192704
%N First differences of A135094.
%C Apart to offset same as A136488.
%H G. C. Greubel, <a href="/A135098/b135098.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-4).
%F From _R. J. Mathar_, Feb 15 2008: (Start)
%F O.g.f.: (2*x+1) / (2*(2*x^2-1)) -3 / (2*(2*x-1)).
%F a(n) = (-A016116(n+1) +A007283(n)) / 2 . (End)
%F G.f.: (1 - x)*(1 + x) / ((1 - 2*x)*(1 - 2*x^2)). - _Arkadiusz Wesolowski_, Oct 24 2013
%F From _G. C. Greubel_, Sep 23 2016: (Start)
%F a(n) = 2^((n-5)/2)*( 3*2^((n+1)/2) - (1 - (-1)^n) - (1 + (-1)^n)*sqrt(2) ).
%F E.g.f.: (1/4)*( 3*exp(2*x) - 2*cosh(sqrt(2)*x) - sqrt(2)*sinh(sqrt(2)*x). (End)
%F a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3). - _Wesley Ivan Hurt_, Apr 07 2021
%t 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 *)
%o (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
%Y Cf. A135094, A136488 (same up to offset).
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Feb 12 2008
%E More terms from _R. J. Mathar_, Feb 15 2008
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