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A132971
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a(2*n) = a(n), a(4*n+1) = -a(n), a(4*n+3) = 0.
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0
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1, -1, -1, 0, -1, 1, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, -1, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, -1, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 1, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| If binary(n) has adjacent 1 bits then a(n) = 0 else a(n) = (-1)^A000120(n).
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REFERENCES
| Paul Tarau, Emulating Primality with Multiset Representations of Natural Numbers, in THEORETICAL ASPECTS OF COMPUTING, ICTAC 2011, Lecture Notes in Computer Science, 2011, Volume 6916/2011, 218-238, DOI: 10.1007/978-3-642-23283-1_15; http://www.springerlink.com/content/x0044261g7004717/.
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FORMULA
| A024490(n) = number of solutions to 2^n <= k < 2^(n+1) and a(k) = 1.
A005252(n) = number of solutions to 2^n <= k < 2^(n+1) and a(k) = -1.
A027935(n-1) = number of solutions to 2^n <= k < 2^(n+1) and a(k) = 0.
G.f. A(x) satisfies A(x) = A(x^2) - x * A(x^4).
G.f. B(x) of A000621 satisfies B(x) = x * A(x^2) / A(x).
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EXAMPLE
| 1 - x - x^2 - x^4 + x^5 - x^8 + x^9 + x^10 - x^16 + x^17 + x^18 + ...
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PROG
| (PARI) {a(n) = if( n<1, n==0, if( n%2, if( n%4 > 1, 0, -a((n-1)/4) ), a(n/2) ) )}
(PARI) {a(n) = local(A, m); if( n<0, 0, m = 1; A = 1 + O(x); while( m<=n, m *= 2; A = subst(A, x, x^2) - x * subst(A, x, x^4) ); polcoeff( A, n )) }
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CROSSREFS
| Sequence in context: A097806 A167374 A085357 * A011748 A145361 A130304
Adjacent sequences: A132968 A132969 A132970 * A132972 A132973 A132974
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Sep 17 2007, Sep 19 2007
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