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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified January 25 12:16 EST 2022. Contains 350572 sequences. (Running on oeis4.)