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

Author

N. J. A. Sloane, Dec 03 2003

Keywords

• nonn

Comments

The powers do not need to be distinct.

Links

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

Crossrefs

A column of A089052.

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

Programs

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 *)

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