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A067868 a(n) = a(n-1) + a(floor(n/2))^2 for n > 0, a(0) = 1.

%I A067868 #15 Jul 02 2025 19:27:25
%S A067868 1,2,6,10,46,82,182,282,2398,4514,11238,17962,51086,84210,163734,
%T A067868 243258,5993662,11744066,32120262,52496458,178789102,305081746,
%U A067868 627715190,950348634,3560128030,6169907426,13261231526,20352555626,47161378382,73970201138,133144655702,192319110266
%N A067868 a(n) = a(n-1) + a(floor(n/2))^2 for n > 0, a(0) = 1.
%H A067868 G. C. Greubel, <a href="/A067868/b067868.txt">Table of n, a(n) for n = 0..1000</a>
%t A067868 a[n_]:= a[n] = If[n==0, 1, a[n-1] + (a[Floor[n/2]])^2];
%t A067868 Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Feb 10 2021 *)
%o A067868 (PARI) a(n) = if (n==0, 1, a(n-1)+a(n\2)^2);
%o A067868 (Sage)
%o A067868 def a(n): return 1 if n == 0 else a(n-1) + (a(n//2))^2
%o A067868 [a(n) for n in range(50)] # _G. C. Greubel_, Feb 10 2021
%o A067868 (Magma) [1] cat [n le 2 select Factorial(n+1) else Self(n-1) + (Self(Floor(n/2)))^2: n in [1..51]]; // _G. C. Greubel_, Feb 10 2021
%Y A067868 Cf. A000123, A056520, A058039.
%K A067868 nonn
%O A067868 0,2
%A A067868 _Reinhard Zumkeller_, Feb 16 2002
%E A067868 Corrected name and more terms from _Michel Marcus_, Feb 05 2021