A058039 a(n) = a(n-1) + 2*a(floor(n/2)) if n > 0, otherwise 1.

1, 3, 9, 15, 33, 51, 81, 111, 177, 243, 345, 447, 609, 771, 993, 1215, 1569, 1923, 2409, 2895, 3585, 4275, 5169, 6063, 7281, 8499, 10041, 11583, 13569, 15555, 17985, 20415, 23553, 26691, 30537, 34383, 39201, 44019, 49809, 55599, 62769, 69939, 78489, 87039

Offset

0,2

Links

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

Formula

a(n) = 1 + 2 * Sum_{k=1..n} a(floor(k/2)). - Ilya Gutkovskiy, Aug 15 2021

Mathematica

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

Prog

(PARI) a(n) = if (n==0, 1, a(n-1)+2*a(n\2)); \\ Michel Marcus, Feb 04 2021
(Python)
def a(n): return 1 if n == 0 else a(n-1) + 2*a(n//2)
print([a(n) for n in range(44)]) # Michael S. Branicky, Feb 04 2021
(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

Crossrefs

Cf. A000123, A002061, A067868, A347027.

Sequence in context: A061810 A048701 A031159 * A371349 A013581 A350536

Adjacent sequences: A058036 A058037 A058038 * A058040 A058041 A058042

Keyword

nonn

Author

Reinhard Zumkeller, Feb 16 2002

Extensions

Name corrected by and more terms from Michael S. Branicky, Feb 04 2021

Status

approved