A077870 - OEIS

%I #31 Apr 15 2020 11:40:16

%S 1,2,3,2,-1,-6,-9,-6,7,26,39,26,-25,-102,-153,-102,103,410,615,410,

%T -409,-1638,-2457,-1638,1639,6554,9831,6554,-6553,-26214,-39321,

%U -26214,26215,104858,157287,104858,-104857,-419430,-629145,-419430,419431,1677722,2516583,1677722,-1677721,-6710886

%N Expansion of (1-x)^(-1)/(1-x+2*x^3).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-2,2).

%F G.f.: G(0)/(1 + x) where G(k) = 1 + 8*x + 2*k*x + k - 2*x*(k+1)*(k+5)/G(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Apr 09 2013

%F G.f.: G(0)/(2*(1-x^2)*(1-x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 25 2013

%F a(n) = Sum_{k=0..floor((n+1)/2)} (-2)^k*binomial(n+1-2k,k+1), n>=0. - _Taras Goy_, Apr 15 2020

%t LinearRecurrence[{2,-1,-2,2},{1,2,3,2},50] (* _Harvey P. Dale_, Jul 28 2019 *)

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2002