A197432 a(n) = Sum_{k>=0} A030308(n,k)*C(k) where C(k) is the k-th Catalan number (A000108).

0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 42, 43, 43, 44, 44, 45, 45, 46, 47, 48, 48, 49, 49, 50, 50, 51, 56, 57, 57, 58, 58, 59, 59, 60, 61, 62, 62, 63, 63, 64, 64, 65

Offset: 0

Author

Philippe Deléham, Oct 15 2011

Keywords

• nonn
• easy

Comments

Replace 2^k with A000108(k) in binary expansion of n.

Examples

			11 = 1011_2, so a(11) = 1*1 + 1*1 + 0*2 + 1*5 = 7.
		

Crossrefs

Cf. A000108, A030308, A197433.

Other sequences that are built by replacing 2^k in binary representation with other numbers: A022290 (Fibonacci), A029931 (natural numbers), A059590 (factorials), A089625 (primes), A197354 (odd numbers).

Formula

G.f.: (1/(1 - x))*Sum_{k>=0} Catalan number(k)*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jul 23 2017