Search: id:A105348
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%I A105348
%S A105348 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,
%T A105348 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,
%U A105348 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
%N A105348 An indicator sequence for the Jacobsthal numbers.
%C A105348 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
%F A105348 G.f. : sum{k>=0, x^A001045(k)}
%F A105348 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
%e A105348 a(1)=2 since J(1)=J(2)=1.
%Y A105348 For partial sums see A130253. Cf. A130249, A130250.
%Y A105348 Sequence in context: A075120 A111593 A111594 this_sequence A016406 A129182 
               A116857
%Y A105348 Adjacent sequences: A105345 A105346 A105347 this_sequence A105349 A105350 
               A105351
%K A105348 easy,nonn
%O A105348 0,2
%A A105348 Paul Barry (pbarry(AT)wit.ie), Apr 01 2005

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