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a(0)=0, a(1)=1, a(n)=min{3 a(k) + 2^(n-k)-1, k=0..(n-1)} for n>=2.
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%I #25 Mar 16 2021 04:59:53

%S 0,1,3,6,10,16,24,33,45,61,79,103,130,162,198,246,300,364,436,517,613,

%T 721,849,993,1155,1347,1563,1806,2062,2350,2674,3058,3490,3976,4488,

%U 5064,5712,6441,7209,8073,9045,10069,11221,12517,13975,15511,17239,19183

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

%C The sequence of first differences is A003586.

%H Gheorghe Coserea and Reinhard Zumkeller, <a href="/A259823/b259823.txt">Table of n, a(n) for n = 0..10000</a>, First 4096 terms from Gheorghe Coserea

%H Thierry Bousch, <a href="https://www.emis.de/journals/SLC/wpapers/s77bousch.html">La Tour de Stockmeyer</a>, Séminaire Lotharingien de Combinatoire 77 (2017), Article B77d.

%H Jonathan Chappelon and Akihiro Matsuura, <a href="http://arxiv.org/abs/1009.0146">On generalized Frame-Stewart numbers</a>, arXiv:1009.0146 [math.NT], 2010.

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

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

%t 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}]

%o (Haskell)

%o a259823 n = a259823_list !! n

%o a259823_list = scanl (+) 0 a003586_list

%o -- _Reinhard Zumkeller_, Jul 19 2015

%Y Cf. A003586, A291876.

%K nonn

%O 0,3

%A _Gheorghe Coserea_, Jul 05 2015