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A330714 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * i^k (where i denotes the imaginary unit); a(n) is the square of the modulus of h(n).

%I A330714 #27 May 06 2021 03:17:25
%S A330714 0,1,1,2,1,0,2,1,1,2,0,1,2,1,1,0,1,4,2,5,0,1,1,2,2,5,1,4,1,2,0,1,1,2,
%T A330714 4,5,2,1,5,4,0,1,1,2,1,0,2,1,2,5,5,8,1,2,4,5,1,4,2,5,0,1,1,2,1,0,2,1,
%U A330714 4,1,5,2,2,1,1,0,5,2,4,1,0,1,1,2,1
%N A330714 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * i^k (where i denotes the imaginary unit); a(n) is the square of the modulus of h(n).
%H A330714 Seiichi Manyama, <a href="/A330714/b330714.txt">Table of n, a(n) for n = 0..10000</a>
%H A330714 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A330714 a(n) = A131851(n)^2 + A131852(n)^2.
%t A330714 a[0] = 0; a[n_] := a[n] = a[Floor[n/2]]*I + Mod[n, 2]; Table[Abs[a[n]]^2, {n, 0, 100}] (* _Amiram Eldar_, May 06 2021, after _Jean-François Alcover_ at A131851 *)
%o A330714 (PARI) {a(n) = my(d=Vecrev(digits(n, 2))); norm(sum(k=1, #d, d[k]*I^k))}
%Y A330714 Cf. A007088, A131851, A131852, A131853, A131856, A131858, A131860, A290886, A318479.
%K A330714 nonn,base
%O A330714 0,4
%A A330714 _Seiichi Manyama_, Dec 27 2019