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Search: id:A005536
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| A005536 |
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a(0) = 0, a(2n) = n-a(n)-a(n-1), a(2n+1) = n-2a(n)+1.
(Formerly M2274)
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+0
5
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| 1, 0, 0, 1, 3, 3, 4, 3, 3, 1, 0, 0, 1, 0, 0, 1, 3, 3, 4, 6, 9, 10, 12, 12, 13, 12, 12, 13, 15, 15, 16, 15, 15, 13, 12, 12, 13, 12, 12, 10, 9, 6, 4, 3, 3, 1, 0, 0, 1, 0, 0, 1, 3, 3, 4, 3, 3, 1, 0, 0, 1, 0, 0, 1, 3, 3, 4, 6, 9, 10, 12, 12, 13, 12, 12, 13, 15, 15, 16, 18, 21, 22, 24, 27, 31, 33
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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A "Von Koch" sequence generated by the first Feigenbaum symbolic sequence.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
R. G. Stanton, W. L. Kocay and P. H. Dirksen, Computation of a combinatorial function, pp. 569-578 of C. J. Nash-Williams and J. Sheehan, editors, Proceedings of the Fifth British Combinatorial Conference 1975. Utilitas Math., Winnipeg, 1976.
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LINKS
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J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences related to binary expansion of n
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FORMULA
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Partial sums of A065359. a(n)=sum(i=0, n, sum(k=0, i, (-1)^k*(floor(i/2^k)-2*floor(i/2/2^k)))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 28 2004
G.f. 1/(1-x)^2 * Sum(k>=0, (-1)^k*x^2^k/(1+x^2^k)). - Ralf Stephan, Apr 27 2003
a(n) = -n*(n-2) + 3*sum(k=1, n-1, sum(i=1, k, A035263(i+1))), where A035263 is the first Feigenbaum symbolic sequence. - Benoit Cloitre, May 29 2003
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PROGRAM
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(PARI) a(n)=-n*(n-2)+3*sum(k=1, n-1, sum(i=1, k, abs(subst(Pol(binary(i+1))- Pol(binary(i)), x, 1)%2))) (from B. Cloitre)
(PARI) a(n)=polcoeff(1/(1-x)^2*sum(k=0, 10, (-1)^k*x^2^k/(1+x^2^k)) +O(x^(n+1)), n)
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CROSSREFS
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Cf. A071992, A073059.
Sequence in context: A159636 A023647 A082978 this_sequence A080038 A121937 A003034
Adjacent sequences: A005533 A005534 A005535 this_sequence A005537 A005538 A005539
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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).
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EXTENSIONS
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More terms and better description from Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 13 2003
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