A184617 With nonadjacent forms: A184615(n) + A184616(n).

0, 1, 2, 5, 4, 5, 10, 9, 8, 9, 10, 21, 20, 21, 18, 17, 16, 17, 18, 21, 20, 21, 42, 41, 40, 41, 42, 37, 36, 37, 34, 33, 32, 33, 34, 37, 36, 37, 42, 41, 40, 41, 42, 85, 84, 85, 82, 81, 80, 81, 82, 85, 84, 85, 74, 73, 72, 73, 74, 69, 68, 69, 66, 65, 64, 65, 66, 69, 68, 69, 74, 73, 72, 73, 74, 85, 84, 85, 82, 81, 80, 81, 82

Offset: 0

Author

Joerg Arndt, Jan 18 2011

Keywords

• nonn
• look

Comments

No two adjacent bits in the binary representations of a(n) are 1.

The value 0 appears once, otherwise, if the binary representation of a(n) has k set bits then it appears 2^(k-1) times.

Examples

			See A184615.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10922
• Joerg Arndt, Matters Computational (The Fxtbook), pages 61-62.

Crossrefs

Cf. A178729.

Cf. A184615 (positive parts), A184616 (negated negative parts).

Programs

Mathematica

a[n_] := Module[{nh, n3, c}, nh = BitShiftRight[n]; n3 = n + nh; c = BitXor[nh, n3]; BitAnd[n3, c] + BitAnd[nh, c]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 30 2019, from PARI code in A184615 *)

PARI

(see A184615)

Python

for n in range(77):
  print((n^(n*3))/2, end=',')
# Alex Ratushnyak, Aug 13 2012

Formula

a(n) = A184615(n) + A184616(n).

a(n) = A178729(n)/2 = (n XOR n*3)/2. Note a(2^n) = 2^n. - Alex Ratushnyak, Aug 13 2012