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A105348
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An indicator sequence for the Jacobsthal numbers.
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9
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1, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is the number of solutions to the Diophantine equation 2x^2-(9n+1)x+9n^2=1 where valid solutions are restricted to powers of 4. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007
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FORMULA
| G.f. : sum{k>=0, x^A001045(k)}
a(n)=1+floor(log_2(3n+1))-ceiling(log_2(3n-1))=floor(log_2(3n+1))-floor(log_2(3n-2)) for n>=1. Also true: a(n)=1+A130249(n)-A130250(n))=A130253(n)-A130250(n)=A130250(n+1)-A13050(n) for n>=0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007
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EXAMPLE
| a(1)=2 since J(1)=J(2)=1.
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CROSSREFS
| For partial sums see A130253. Cf. A130249, A130250.
Sequence in context: A111593 A111594 A203951 * A016406 A129182 A116857
Adjacent sequences: A105345 A105346 A105347 * A105349 A105350 A105351
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
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