A129099 a(n) = Sum_{k=2^(n-1)..2^n-1} A129095(k) for n>=1.

1, 4, 20, 136, 1376, 22176, 591680, 26770688, 2096125184, 289083462144, 71239716616192, 31730665042094080, 25779103986580017152, 38488216155785101459456, 106257557996370396596748288, 545336631331873524033714683904

Offset: 1

Author

Paul D. Hanna, Apr 11 2007

Keywords

• easy
• nonn

Comments

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.

Crossrefs

Cf. A129095, A129096, A129097, A129098.

Programs

Mathematica

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 *)

PARI

Formula

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

Extensions

a(16) from Michael De Vlieger, Mar 10 2020