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A323365 Sum of Stern's Diatomic sequence, A002487 and its Dirichlet inverse, A317843.

%I A323365 #13 Dec 09 2021 01:30:43
%S A323365 2,0,0,1,0,4,0,1,4,6,0,2,0,6,12,1,0,4,0,3,12,10,0,2,9,10,8,3,0,-4,0,1,
%T A323365 20,10,18,4,0,14,20,3,0,4,0,5,4,14,0,2,9,5,20,5,0,8,30,3,28,14,0,4,0,
%U A323365 10,20,1,30,-8,0,5,28,0,0,4,0,22,-2,7,30,0,0,3,16,22,0,8,30,26,28,5,0,20,30,7,20,18,42,2,0,9,4,7,0,4,0,5,0
%N A323365 Sum of Stern's Diatomic sequence, A002487 and its Dirichlet inverse, A317843.
%H A323365 Antti Karttunen, <a href="/A323365/b323365.txt">Table of n, a(n) for n = 1..16384</a>
%H A323365 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A323365 a(n) = A002487(n) + A317843(n).
%F A323365 From _Antti Karttunen_, Dec 08 2021: (Start)
%F A323365 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A002487(d) * A317843(n/d).
%F A323365 a(4*n) = A002487(n).
%F A323365 (End)
%o A323365 (PARI)
%o A323365 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A323365 A317843(n) = if(1==n,1,-sumdiv(n,d,if(d<n,A002487(n/d)*A317843(d),0)));
%o A323365 A323365(n) = (A002487(n) + A317843(n));
%Y A323365 Cf. A002487 (also a quadrisection of this sequence), A317843.
%Y A323365 Cf. also A317837, A319687, A323885, A323887, A323894, A323896.
%K A323365 sign,look
%O A323365 1,1
%A A323365 _Antti Karttunen_, Jan 13 2019