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A087810
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First differences of A029931.
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0
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1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -5, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -9, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -5, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -14, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -5, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| Multiplicative with a(2^e) = 1-A000217(e-1), a(p^e) = 1 otherwise. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) May 17, 2005.
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FORMULA
| a(4n) = 1 - T(v_2(n)), else a(n) = 1, where T = A000217 (triangular numbers) and v_2 = A007814 (exponent of 2 in factorization of n).
G.f.: sum(k>=0, (k+1)t/(1+t), t=x^2^k).
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PROG
| (PARI) a(n)=if(n<1, 0, if(n%2==0, if(n%4, 1, 1-valuation(n, 2)*(valuation(n, 2)-1)/2), 1))
(PARI) a(n)=polcoeff(sum(k=0, floor(log2(n)), (k+1)*x^2^k/(1+x^2^k)), n)
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CROSSREFS
| Sequence in context: A194087 A107034 A117410 * A052314 A093718 A035212
Adjacent sequences: A087807 A087808 A087809 * A087811 A087812 A087813
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KEYWORD
| sign,easy,mult
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 16 2003
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