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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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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
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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 *) -
PARI
a(n) = if (n==0, 1, a(n-1)+2*a(n\2)); \\ Michel Marcus, Feb 04 2021
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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
Formula
a(n) = 1 + 2 * Sum_{k=1..n} a(floor(k/2)). - Ilya Gutkovskiy, Aug 15 2021
Extensions
Name corrected by and more terms from Michael S. Branicky, Feb 04 2021