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%I #22 Jul 18 2022 20:13:28
%S 0,1,4,7,16,25,34,61,88,115,142,223,304,385,466,547,790,1033,1276,
%T 1519,1762,2005,2734,3463,4192,4921,5650,6379,7108,9295,11482,13669,
%U 15856,18043,20230,22417,24604,31165,37726,44287,50848,57409,63970,70531,77092
%N a(0)=0, a(1)=1, a(n) = min{3 a(k) + (3^(n-k)-1)/2, k=0..(n-1)} for n>=2.
%C A generalization of Frame-Stewart recurrence is a(0)=0, a(1)=1, a(n)=min{q*a(k) + (q^(n-k)-1)/(q-1), k=0..(n-1)} where n>=2 and q>1. The sequence of first differences is q^A003056(n). For q=2 we have the sequence A007664. The current sequence is generated for q=3.
%H Gheorghe Coserea, <a href="/A259653/b259653.txt">Table of n, a(n) for n = 0..4096</a>
%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.
%H P. Stockmeyer, <a href="http://www.cs.wm.edu/~pkstoc/boca.pdf">Variations on the Four-Post Tower of Hanoi Puzzle</a>
%F a(n) = min {3*a(k) + (3^(n-k)-1)/2 ; k < n}.
%F a(n) = sum(3^A003056(i), i=0..n-1).
%t a[n_] := a[n] = Min[ Table[ 3*a[k] + (3^(n-k) - 1)/2, {k, 0, n-1}]]; a[0] = 0; Table[a[n], {n, 0, 60}]
%Y Cf. A003056, A007664.
%Y Essentially partial sums of A098355.
%K nonn
%O 0,3
%A _Gheorghe Coserea_, Jul 02 2015
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