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Search: id:A005766
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| A005766 |
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a(n) = cost of minimal multiplication-cost addition chain for n.
(Formerly M2448)
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+0
5
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| 0, 1, 3, 5, 9, 12, 18, 21, 29, 34, 44, 48, 60, 67, 81, 85, 101, 110, 128, 134, 154, 165, 187, 192, 216, 229, 255, 263, 291, 306, 336, 341, 373, 390, 424, 434, 470, 489, 527, 534, 574, 595, 637, 649, 693, 716, 762, 768, 816, 841, 891, 905, 957, 984, 1038
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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R. L. Graham et al., Addition chains with multiplicative cost, Discrete Math., 23 (1978), 115-119.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197, ex. 21.
R. L. Graham et al., Addition chains with multiplicative cost [Cached copy]
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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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
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
a(n) = sum(k=1, n, A007814(n) + 2*A025480(n-1)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 30 2003
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PROGRAM
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(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))
(PARI) a(n)=sum(k=1, n, valuation(k, 2)+k/2^valuation(k, 2)-1)
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CROSSREFS
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Partial sums of A089265.
Sequence in context: A086845 A127722 A060419 this_sequence A046746 A058599 A059093
Adjacent sequences: A005763 A005764 A005765 this_sequence A005767 A005768 A005769
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), May 04 2003
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