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a(n) = 2^(floor(n/2))+2^(floor(n/2)-1)-2^(floor((n-1)/3)).
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%I #16 Jul 04 2018 01:56:33

%S 2,2,4,4,10,8,20,20,40,40,88,80,176,176,352,352,736,704,1472,1472,

%T 2944,2944,6016,5888,12032,12032,24064,24064,48640,48128,97280,97280,

%U 194560,194560,391168,389120,782336,782336,1564672,1564672,3137536,3129344,6275072

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

%H R. P. Stanley, <a href="https://www.jstor.org/stable/10.4169/000298910x475032">Problem 11348</a>, Amer. Math. Monthly, 117 (2010), 87-88.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,0,-4).

%F a(n) = 2*a(n-2)+2*a(n-3)-4*a(n-5). G.f.: -2*x^2*(x^4+2*x^3-x-1) / ((2*x^2-1)*(2*x^3-1)). - _Colin Barker_, Jul 25 2013

%Y Cf. A170832, A170833, A170834.

%K nonn,easy

%O 2,1

%A _N. J. A. Sloane_, Dec 30 2009