%I #23 Aug 15 2021 21:53:09

%S 1,3,9,15,33,51,81,111,177,243,345,447,609,771,993,1215,1569,1923,

%T 2409,2895,3585,4275,5169,6063,7281,8499,10041,11583,13569,15555,

%U 17985,20415,23553,26691,30537,34383,39201,44019,49809,55599,62769,69939,78489,87039

%N a(n) = a(n-1) + 2*a(floor(n/2)) if n > 0, otherwise 1.

%H G. C. Greubel, <a href="/A058039/b058039.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 1 + 2 * Sum_{k=1..n} a(floor(k/2)). - _Ilya Gutkovskiy_, Aug 15 2021

%t a[n_]:= a[n] = If[n==0, 1, a[n-1] + 2*a[Floor[n/2]]];

%t Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Feb 10 2021 *)

%o (PARI) a(n) = if (n==0, 1, a(n-1)+2*a(n\2)); \\ _Michel Marcus_, Feb 04 2021

%o (Python)

%o def a(n): return 1 if n == 0 else a(n-1) + 2*a(n//2)

%o print([a(n) for n in range(44)]) # _Michael S. Branicky_, Feb 04 2021

%o (Magma) [1] cat [n le 2 select 3^n else Self(n-1) + 2*Self(Floor(n/2)): n in [1..51]]; // _G. C. Greubel_, Feb 10 2021

%Y Cf. A000123, A002061, A067868, A347027.

%K nonn

%O 0,2

%A _Reinhard Zumkeller_, Feb 16 2002

%E Name corrected by and more terms from _Michael S. Branicky_, Feb 04 2021