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A078903
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a(n)=n^2-sum(u=1,n,sum(v=1,u,valuation(2*v,2))).
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3
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0, 0, 1, 1, 2, 3, 5, 5, 6, 7, 9, 10, 12, 14, 17, 17, 18, 19, 21, 22, 24, 26, 29, 30, 32, 34, 37, 39, 42, 45, 49, 49, 50, 51, 53, 54, 56, 58, 61, 62, 64, 66, 69, 71, 74, 77, 81, 82, 84, 86, 89, 91, 94, 97, 101, 103, 106, 109, 113, 116, 120, 124, 129, 129, 130, 131, 133, 134
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| A fractal generator sequence. Let Fr(m,n) = m*n-a(n); then the graph of Fr(m,n) for 1<=n<=4^(m+1)-3 presents fractal aspects.
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LINKS
| R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
| a(n)=n^2-sum(k=1, n, A005187(k)); a(n)=n^2-sum(u=1, n, sum(v=1, u, A001511(v))); a(n+1)-a(n)= A048881(n)
G.f.: 1/(1-x)^2 * ((x(1+x)/(1-x) - Sum(k>=0, x^2^k/(1-x^2^k)))). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 12 2002
a(0) = 0, a(2n) = a(n) + a(n-1) + n - 1, a(2n+1) = 2a(n) + n. a(n) = A000788(n) - n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 05 2003
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EXAMPLE
| Fr(1, n) for 1<=n<=4^2-3=13 gives : 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 1; Fr(2, n) for 1<=n<=4^3-3=63 gives : 2, 4, 5, 7, 8, 9, 9, 11, 12, 13, 13, 14, 14, 14, 13, 15, 16, 17, 17, 18, 18, 18, 17, 18, 18, 18, 17, 17, 16, 15, 13, 15, 16, 17, 17, 18, 18, 18, 17, 18, 18, 18, 17, 17, 16, 15, 13, 14, 14, 14, 13, 13, 12, 11, 9, 9, 8, 7, 5, 4, 2
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PROG
| (PARI) a(n)=n^2-sum(u=1, n, sum(v=1, u, valuation(2*v, 2)))
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CROSSREFS
| Cf. A078904, A073504.
Equals 1/2 * A076178(n).
Sequence in context: A111164 A029910 A063677 * A079228 A067535 A076752
Adjacent sequences: A078900 A078901 A078902 * A078904 A078905 A078906
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 12 2002
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