A229898 Number of c-squarefree numbers (A233564) less than 2^n.

0, 1, 2, 5, 8, 13, 24, 37, 56, 83, 140, 205, 306, 439, 632, 983, 1418, 2035, 2886, 4063, 5618, 8369, 11666, 16423, 22716, 31477, 42782, 58385, 82700, 113161, 155028, 210769, 285644, 383687, 514496, 682921, 940326, 1256299, 1687364, 2245691, 2997182, 3955447, 5233314

Offset: 0

Author

Vladimir Shevelev, Dec 19 2013

Keywords

• nonn
• base

Comments

For n >= 1, a(n) is the total number of compositions of positive integers less than or equal to n with distinct parts (cf. A032020).

For example, numbers of such compositions of 1,2,3,4,5 are 1,1,3,3,5. So a(5)=13.

Links

• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A233564, A032020.

Formula

a(n) - a(n-1) = A032020(n).

G.f.: (1/(1 - x)) * Sum_{i>=1} i!*x^(i*(i+1)/2) * Product_{j=1..i} 1/(1 - x^j). - Ilya Gutkovskiy, Apr 04 2017

Extensions

More terms from Peter J. C. Moses, Dec 19-20 2013