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A005942
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a(2n)=a(n)+a(n+1), a(2n+1)=2a(n+1), if n>1.
(Formerly M1007)
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6
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1, 2, 4, 6, 10, 12, 16, 20, 22, 24, 28, 32, 36, 40, 42, 44, 46, 48, 52, 56, 60, 64, 68, 72, 76, 80, 82, 84, 86, 88, 90, 92, 94, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. Berstel et al., Combinatorics on Words: Christoffel Words and Repetitions in Words, Amer. Math. Soc., 2008. See p. 83.
S. Brlek, Enumeration of factors in the Thue-Morse word, Discrete Applied Math., 24 (1989), 83-96. doi:10.1016/0166-218X(92)90274-E
De Luca, Aldo; Varricchio, Stefano; Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups. Theoret. Comput. Sci. 63 (1989), no. 3, 333-348. doi:10.1016/0304-3975(89)90013-3
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
| a(n) = 2*(A006165(n-1) + n - 1), n>1.
G.f. (1+x^2)/(1-x)^2 + 2x^2/(1-x)^2 * sum(k>=0, x^2^(k+1)-x^(3*2^k)). - Ralf Stephan, Jun 04 2003
For n>2, a(n) = 3*(n-1) + A053646(n-1). [From Max Alekseyev, May 15 2011]
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MATHEMATICA
| a[0] = 1; a[1] = 2; a[2] = 4; a[3] = 6; a[n_?EvenQ] := a[n] = a[n/2] + a[n/2 + 1]; a[n_?OddQ] := a[n] = 2*a[(n + 1)/2]; Array[a, 60, 0] (* From Jean-François Alcover, Apr 11 2011 *)
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PROG
| (PARI) a(n)=if(n<4, 2*max(0, n)+(n==0), if(n%2, 2*a((n+1)/2), a(n/2)+a(n/2+1)))
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CROSSREFS
| Cf. A005943, A006697.
Sequence in context: A178539 A072752 A036634 * A024907 A033098 A033868
Adjacent sequences: A005939 A005940 A005941 * A005943 A005944 A005945
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
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