A089048 Number of ways of writing n as a sum of exactly 3 powers of 2.

0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 0, 1

Offset

0,7

Comments

The powers do not need to be distinct.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

For n > 2: a(n) = (1 + (1 - A000120(n) mod 2)*(1 - n mod 2)) * 0^floor(A000120(n)/4). - Reinhard Zumkeller, Dec 14 2003

Maple

f := proc(n, k) option remember; if k > n then RETURN(0); fi; if k= 0 then if n=0 then RETURN(1) else RETURN(0); fi; fi; if n mod 2 = 1 then RETURN(f(n-1, k-1)); fi; f(n-1, k-1)+f(n/2, k); end; # present sequence is f(n, 3)

Mathematica

a[n_] := If[n < 3, 0, ((1 - Mod[n, 2])*(1 - Mod[DigitCount[n, 2, 1], 2]) + 1)*If[Floor[(1/4)*DigitCount[n, 2, 1]] == 0, 1, 0]];
Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Feb 13 2018, after Reinhard Zumkeller *)

Crossrefs

A column of A089052.

Cf. A000120, A036987, A075897, A089049, A089050, A089051, A089053.

Sequence in context: A305054 A238097 A066955 * A329443 A348416 A263025

Adjacent sequences: A089045 A089046 A089047 * A089049 A089050 A089051

Keyword

nonn

Author

N. J. A. Sloane, Dec 03 2003

Status

approved