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

1, 2, 6, 10, 46, 82, 182, 282, 2398, 4514, 11238, 17962, 51086, 84210, 163734, 243258, 5993662, 11744066, 32120262, 52496458, 178789102, 305081746, 627715190, 950348634, 3560128030, 6169907426, 13261231526, 20352555626, 47161378382, 73970201138, 133144655702, 192319110266

Offset: 0

Author

Reinhard Zumkeller, Feb 16 2002

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000123, A056520, A058039.

Programs

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

Mathematica

a[n_]:= a[n] = If[n==0, 1, a[n-1] + (a[Floor[n/2]])^2];
Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 10 2021 *)

PARI

a(n) = if (n==0, 1, a(n-1)+a(n\2)^2);

Sage

def a(n): return 1 if n == 0 else a(n-1) + (a(n//2))^2
[a(n) for n in range(50)] # G. C. Greubel, Feb 10 2021

Extensions

Corrected name and more terms from Michel Marcus, Feb 05 2021