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%I #11 Feb 16 2020 07:56:14
%S 1,-1,-2,0,-3,2,-3,0,0,3,-5,0,-5,3,8,0,-5,0,-7,0,4,5,-7,0,2,5,0,0,-7,
%T -8,-5,0,14,5,9,0,-11,7,10,0,-11,-4,-13,0,-8,7,-9,0,0,-2,8,0,-13,0,19,
%U 0,18,7,-11,0,-9,5,14,0,23,-14,-11,0,14,-9,-13,0,-15,11,-20,0,13,-10,-13,0,2,11,-19,0,9,13,10,0,-17,8,11,0
%N Dirichlet inverse of Stern's diatomic sequence (A002487).
%H Antti Karttunen, <a href="/A317843/b317843.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F a(1) = 1; for n > 1, a(n) = -Sum_{d|n, d<n} A002487(n/d)*a(d).
%t s[0] = 0; s[1] = 1;
%t s[n_] := s[n] = If[EvenQ[n], s[n/2], s[(n-1)/2] + s[(n+1)/2]];
%t a[n_] := a[n] = If[n == 1, 1, -Sum[s[n/d] a[d], {d, Most@ Divisors[n]}]];
%t Array[a, 100] (* _Jean-François Alcover_, Feb 16 2020 *)
%o (PARI)
%o A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A317843(n) = if(1==n,1,-sumdiv(n,d,if(d<n,A002487(n/d)*A317843(d),0)));
%Y Cf. A002487, A317839, A317841, A317842.
%K sign
%O 1,3
%A _Antti Karttunen_, Aug 09 2018
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