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a(1) = 1, a(m+1) = 2*Sum_{k=1..floor((m+1)/2)} a(k).
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%I #22 Dec 12 2017 00:30:53

%S 1,2,2,6,6,10,10,22,22,34,34,54,54,74,74,118,118,162,162,230,230,298,

%T 298,406,406,514,514,662,662,810,810,1046,1046,1282,1282,1606,1606,

%U 1930,1930,2390,2390,2850,2850,3446,3446,4042,4042,4854,4854,5666,5666,6694

%N a(1) = 1, a(m+1) = 2*Sum_{k=1..floor((m+1)/2)} a(k).

%H Michael De Vlieger, <a href="/A039722/b039722.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1)=1, a(2)=2, a(2m+1)=a(2m), a(2m+2)=a(2m+1)+2a(m+1) {m is a positive integer.}

%e a(6) = 2*(a(1)+a(2)+a(3)) = 2*(1+2+2) = 10.

%t Fold[Append[#1, 2 Total[#1[[Range[Floor[#2/2] ] ]] ] ] &, {1}, Range[2, 52]] (* _Michael De Vlieger_, Dec 11 2017 *)

%o (PARI) lista(nn) = {v = vector(nn); v[1] = 1; for (n=2, nn, v[n] = 2*sum(k=1, n\2, v[k]);); v;} \\ _Michel Marcus_, May 18 2014

%Y Cf. A039721 (similar definition).

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Dec 11 1999

%E More terms from _Michel Marcus_, May 18 2014