A127981 - OEIS

%I #20 Sep 08 2022 08:45:29

%S 1,4,13,34,85,202,469,1066,2389,5290,11605,25258,54613,117418,251221,

%T 535210,1135957,2402986,5068117,10660522,22369621,46836394,97867093,

%U 204122794,425022805,883600042,1834308949,3802835626,7874106709

%N a(n) = (n + 1/3)*2^(n-1) - 1/2 + (-1)^(n-1)*(1/6).

%H G. C. Greubel, <a href="/A127981/b127981.txt">Table of n, a(n) for n = 1..1000</a>

%H W. Bosma, <a href="http://dx.doi.org/10.5802/jtnb.301">Signed bits and fast exponentiation</a>, Journal de Théorie des Nombres de Bordeaux, Vol. 13, Fasc. 1 (2001), p. 38 (Proposition 7).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-4,4).

%F G.f.: x*(1-2*x^3)/((1-x)*(1+x)*(1-2*x)^2). - _Colin Barker_, Apr 02 2012

%t Table[(n+1/3)*2^(n-1) -1/2 +(-1)^(n-1)*(1/6), {n, 1, 50}]

%t LinearRecurrence[{4,-3,-4,4}, {1,4,13,34}, 50] (* _G. C. Greubel_, May 08 2018 *)

%o (PARI) for(n=1,50, print1((n+1/3)*2^(n-1) -1/2 +(-1)^(n-1)*(1/6), ", ")) \\ _G. C. Greubel_, May 08 2018

%o (Magma) [(n+1/3)*2^(n-1) -1/2 +(-1)^(n-1)*(1/6): n in [1..50]]; // _G. C. Greubel_, May 08 2018

%Y Cf. A073371, A127976, A127978, A127979, A127980, A073371.

%K nonn,easy

%O 1,2

%A _Artur Jasinski_, Feb 09 2007