cp's OEIS Frontend

A318704 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the square of the modulus of f(n).

%I A318704 #9 Sep 02 2018 13:34:37
%S A318704 0,1,1,2,4,1,5,2,4,5,1,2,8,5,5,2,16,25,17,26,4,9,5,10,20,29,17,26,8,
%T A318704 13,5,10,16,17,25,26,20,17,29,26,4,5,9,10,8,5,13,10,32,41,41,50,20,25,
%U A318704 29,34,20,29,25,34,8,13,13,18,64,49,65,50,100,81,101
%N A318704 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the square of the modulus of f(n).
%C A318704 See A318702 for the real part of f and additional comments.
%H A318704 Rémy Sigrist, <a href="/A318704/b318704.txt">Table of n, a(n) for n = 0..16383</a>
%H A318704 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A318704 a(n) = A318702(n)^2 + A318703(n)^2.
%F A318704 a(4 * k) = 4 * a(k) for any k >= 0.
%o A318704 (PARI) a(n) = my (b=Vecrev(binary(n))); norm(sum(k=1, #b, b[k] * I^(k-1) * 2^floor((k-1)/2)))
%Y A318704 Cf. A318702.
%K A318704 nonn,base,look
%O A318704 0,4
%A A318704 _Rémy Sigrist_, Sep 01 2018