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A039722 a(1) = 1, a(m+1) = 2*Sum_{k=1..floor((m+1)/2)} a(k).

%I A039722 #22 Dec 12 2017 00:30:53
%S A039722 1,2,2,6,6,10,10,22,22,34,34,54,54,74,74,118,118,162,162,230,230,298,
%T A039722 298,406,406,514,514,662,662,810,810,1046,1046,1282,1282,1606,1606,
%U A039722 1930,1930,2390,2390,2850,2850,3446,3446,4042,4042,4854,4854,5666,5666,6694
%N A039722 a(1) = 1, a(m+1) = 2*Sum_{k=1..floor((m+1)/2)} a(k).
%H A039722 Michael De Vlieger, <a href="/A039722/b039722.txt">Table of n, a(n) for n = 1..10000</a>
%F A039722 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 A039722 a(6) = 2*(a(1)+a(2)+a(3)) = 2*(1+2+2) = 10.
%t A039722 Fold[Append[#1, 2 Total[#1[[Range[Floor[#2/2] ] ]] ] ] &, {1}, Range[2, 52]] (* _Michael De Vlieger_, Dec 11 2017 *)
%o A039722 (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 A039722 Cf. A039721 (similar definition).
%K A039722 easy,nonn
%O A039722 1,2
%A A039722 _Leroy Quet_, Dec 11 1999
%E A039722 More terms from _Michel Marcus_, May 18 2014