A141747 a(n) is the number of nonnegative integer pairs i,j such that n = 2^i + 3^j.

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

Offset: 1

Author

Clark Kimberling, Jul 01 2008

Keywords

• nonn

Examples

			a(5) = 2, using (i,j) = (1,1) and (2,0).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085634, A141748.

Programs

Maple

f:= proc(n) local j,t,s;
  t:= 0;
  for j from 0 to floor(log[3](n)) do
    s:= n - 3^j;
    if s = 2^padic:-ordp(s,2) then t:= t+1 fi
  od;
  t
end proc:
map(f, [$1..200]); # Robert Israel, Jun 08 2020

Formula

G.f.: ( Sum_{i>=0} x^(2^i) ) * ( Sum_{j>=0} x^(3^j) ). - Ilya Gutkovskiy, Feb 10 2022