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).

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, 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, 4, 1, 5, 2, 2, 1, 1, 0, 5, 2, 4, 1, 0, 1, 1, 2, 1

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Index entries for sequences related to binary expansion of n

Formula

a(n) = A131851(n)^2 + A131852(n)^2.

Mathematica

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 *)

Prog

(PARI) {a(n) = my(d=Vecrev(digits(n, 2))); norm(sum(k=1, #d, d[k]*I^k))}

Crossrefs

Cf. A007088, A131851, A131852, A131853, A131856, A131858, A131860, A290886, A318479.

Sequence in context: A117278 A215556 A140082 * A343640 A293670 A279792

Adjacent sequences: A330711 A330712 A330713 * A330715 A330716 A330717

Keyword

nonn,base

Author

Seiichi Manyama, Dec 27 2019

Status

approved