A134353 - OEIS

%I #22 Dec 27 2018 20:51:57

%S 1,2,8,16,48,96,256,512,1280,2560,6144,12288,28672,57344,131072,

%T 262144,589824,1179648,2621440,5242880,11534336,23068672,50331648,

%U 100663296,218103808,436207616,939524096,1879048192,4026531840,8053063680,17179869184

%N Row sums of triangle A134352.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-8).

%F a(n) = 2^n * A004526(n+2).

%F From _Arkadiusz Wesolowski_, Dec 28 2011: (Start)

%F a(n) = 2^(n-2)*(2*n + 3 + (-1)^n).

%F G.f.: 1/((1 - 2*x)*(1 - 4*x^2)). (End)

%F G.f.: G(0)/(1-x), where G(k)= 1 + 2*x*(k+1)/(k+2 - 2*x*(k+2)*(k+3)/(2*x*(k+3) + (k+1)/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jul 31 2013

%e a(3) = 16 sum of row 3 terms of triangle A134352: (0 + 8 + 0 + 8).

%e a(4) = 48 = 2^4 * A004526(6) = 16 * 3.

%t Table[2^n*((2*n + 3)/4 + (-1)^n/4), {n, 0, 30}] (* _Arkadiusz Wesolowski_, Dec 28 2011 *)

%t LinearRecurrence[{2,4,-8},{1,2,8},40] (* _Harvey P. Dale_, Nov 09 2017 *)

%Y Cf. A134352, A004526.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Oct 21 2007