A259823 a(0)=0, a(1)=1, a(n)=min{3 a(k) + 2^(n-k)-1, k=0..(n-1)} for n>=2.

0, 1, 3, 6, 10, 16, 24, 33, 45, 61, 79, 103, 130, 162, 198, 246, 300, 364, 436, 517, 613, 721, 849, 993, 1155, 1347, 1563, 1806, 2062, 2350, 2674, 3058, 3490, 3976, 4488, 5064, 5712, 6441, 7209, 8073, 9045, 10069, 11221, 12517, 13975, 15511, 17239, 19183

Offset: 0

Author

Gheorghe Coserea, Jul 05 2015

Keywords

• nonn

Comments

The sequence of first differences is A003586.

Links

• Gheorghe Coserea and Reinhard Zumkeller, Table of n, a(n) for n = 0..10000, First 4096 terms from Gheorghe Coserea
• Thierry Bousch, La Tour de Stockmeyer, Séminaire Lotharingien de Combinatoire 77 (2017), Article B77d.
• Jonathan Chappelon and Akihiro Matsuura, On generalized Frame-Stewart numbers, arXiv:1009.0146 [math.NT], 2010.

Crossrefs

Cf. A003586, A291876.

Programs

Haskell

a259823 n = a259823_list !! n
a259823_list = scanl (+) 0 a003586_list
-- Reinhard Zumkeller, Jul 19 2015

Mathematica

a[n_] := a[n] = Min[ Table[ 3*a[k] + 2^(n-k) - 1, {k, 0, n-1}]]; a[0] = 0; Table[a[n], {n, 0, 60}]

Formula

a(n) = min {3*a(k) + 2^(n-k)-1; k < n}.

a(n) = Sum_{i=0..n-1} A003586(i).