A096273 a(0)=0, then a(n)=a(n-1)+(n-1) if n is odd, a(n)=a(n/2)+n/2 otherwise.

0, 0, 1, 3, 3, 7, 6, 12, 7, 15, 12, 22, 12, 24, 19, 33, 15, 31, 24, 42, 22, 42, 33, 55, 24, 48, 37, 63, 33, 61, 48, 78, 31, 63, 48, 82, 42, 78, 61, 99, 42, 82, 63, 105, 55, 99, 78, 124, 48, 96, 73, 123, 63, 115, 90, 144, 61, 117, 90, 148, 78, 138, 109, 171, 63, 127, 96, 162, 82

Offset: 0

Author

Benoit Cloitre, Jun 23 2004

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A010060, A095190.

Programs

Maple

f:= proc(n) option remember;
  if n::odd then procname(n-1)+n-1 else procname(n/2)+n/2 fi
end proc:
f(0):= 0:
map(f, [$0..100]); # Robert Israel, Jan 20 2021

Mathematica

a[0] = 0; a[n_] := a[n] = If[OddQ[n], a[n - 1] + n - 1, a[n/2] + n/2]; Array[a, 100, 0] (* Amiram Eldar, Jul 28 2023 *)

PARI

a(n)=if(n<1,0,if(n%2,a(n-1)+n-1,a(n/2)+(n/2)))

Formula

a(n) mod 2 = A095190(n); a(2n) mod 2 = a(2n+1) mod 2 = A010060(n); a(3n) = 0 mod 3.

G.f. g(x) satisfies g(x) = (1+x)*g(x^2)+x^2*(3*x+1)/(x^2-1)^2. - Robert Israel, Jan 20 2021