%I #6 Mar 10 2020 15:32:00

%S 1,4,20,136,1376,22176,591680,26770688,2096125184,289083462144,

%T 71239716616192,31730665042094080,25779103986580017152,

%U 38488216155785101459456,106257557996370396596748288,545336631331873524033714683904

%N a(n) = Sum_{k=2^(n-1)..2^n-1} A129095(k) for n>=1.

%C b(n)=A129095(n) obeys the recurrence: b(n) = b(n/2) (n even), b(n) = 2*b(n-1) + b(n-2) (n odd >1), with b(1) = 1.

%F a(n) = ( A129097(n+1) - A129097(n) )/2.

%t Block[{e = 16, s}, s = Nest[Append[#1, If[EvenQ[#2], #1[[#2/2]], 2 #1[[-1]] + #1[[-2]] ] ] & @@ {#, Length@ # + 1} &, {1}, 2^e]; Array[Total@ s[[2^# ;; 2^(# + 1) - 1]] &, e, 0] ] (* _Michael De Vlieger_, Mar 10 2020 *)

%o (PARI)

%Y Cf. A129095, A129096, A129097, A129098.

%K easy,nonn

%O 1,2

%A _Paul D. Hanna_, Apr 11 2007

%E a(16) from _Michael De Vlieger_, Mar 10 2020