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a(n) = Sum_{1<=i<j<k<=n} b(i)*b(j)*b(k), where b(m) = A020985(m).
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%I #6 Feb 14 2023 08:54:52

%S 0,0,0,-1,-2,-2,-4,-5,-4,0,8,-5,-12,-14,-16,-17,-20,-20,-16,-25,-22,

%T -14,-28,-21,-34,-40,-40,-45,-46,-42,-52,-49,-40,-24,0,-33,-10,22,-20,

%U 11,52,104,168,91,28,-22,16,-33,-70,-96,-112,-105,-120,-126,-128,-133

%N a(n) = Sum_{1<=i<j<k<=n} b(i)*b(j)*b(k), where b(m) = A020985(m).

%F a(n) = A213626(n)-A213786(n).

%o (Python)

%o def A359045(n): return sum((-1 if (i&(i>>1)).bit_count()&1 else 1)*sum((-1 if (j&(j>>1)).bit_count()&1 else 1)*sum(-1 if (k&(k>>1)).bit_count()&1 else 1 for k in range(j+1,n+1)) for j in range(i+1,n+1)) for i in range(1,n+1))

%Y Cf. A020985, A190173, A213626, A213786, A213787.

%K sign

%O 0,5

%A _Chai Wah Wu_, Feb 12 2023