Search: id:A005766
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%I A005766 M2448
%S A005766 0,1,3,5,9,12,18,21,29,34,44,48,60,67,81,85,101,110,128,134,154,165,187,
%T A005766 192,216,229,255,263,291,306,336,341,373,390,424,434,470,489,527,534,
%U A005766 574,595,637,649,693,716,762,768,816,841,891,905,957,984,1038
%N A005766 a(n) = cost of minimal multiplication-cost addition chain for n.
%D A005766 R. L. Graham et al., Addition chains with multiplicative cost, Discrete 
               Math., 23 (1978), 115-119.
%D A005766 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005766 T. D. Noe, <a href="b005766.txt">Table of n, a(n) for n=1..1000</a>
%H A005766 J.-P. Allouche and J. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/
               Papers/as0.ps">The ring of k-regular sequences</a>, Theoretical Computer 
               Sci., 98 (1992), 163-197, ex. 21.
%H A005766 R. L. Graham et al., <a href="a005766.pdf">Addition chains with multiplicative 
               cost</a> [Cached copy]
%H A005766 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A005766 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%F A005766 a(2n)=a(n)+n^2, a(2n+1)=a(n)+n(n+2). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               May 04 2003
%F A005766 G.f. 1/(1-x) * sum(k>=0, x^2^(k+1)(1+2x^2^k-x^2^(k+1))/(1-x^2^(k+1))^2). 
               - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 27 2003
%F A005766 a(n) = sum(k=1, n, A007814(n) + 2*A025480(n-1)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Oct 30 2003
%o A005766 (PARI) a(n)=if(n<1,0,if(n%2==0,a(n/2)+n^2/4,a((n-1)/2)+(n-1)*(n+3)/4))
%o A005766 (PARI) a(n)=sum(k=1,n,valuation(k,2)+k/2^valuation(k,2)-1)
%Y A005766 Partial sums of A089265.
%Y A005766 Sequence in context: A086845 A127722 A060419 this_sequence A046746 A058599 
               A059093
%Y A005766 Adjacent sequences: A005763 A005764 A005765 this_sequence A005767 A005768 
               A005769
%K A005766 nonn
%O A005766 1,3
%A A005766 N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit, Robert G. 
               Wilson v (rgwv(AT)rgwv.com)
%E A005766 More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), May 04 2003

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