A165417 a(0) = a(1) = 1. For n >=2, a(n) = sum a(k), where k is over the distinct values of the substrings in binary n, and where 0 <= k < n.

1, 1, 2, 1, 4, 4, 5, 2, 8, 8, 8, 9, 14, 14, 12, 4, 16, 16, 16, 17, 20, 16, 23, 20, 36, 36, 36, 37, 42, 42, 28, 8, 32, 32, 32, 33, 32, 36, 39, 36, 48, 48, 32, 42, 64, 60, 57, 44, 88, 88, 88, 89, 96, 88, 97, 96, 128, 128, 128, 130, 116, 116, 64, 16, 64, 64, 64, 65, 64, 68, 71, 68, 72

Offset

0,3

Comments

The distinct nonnegative values of the substrings of binary n is row n of table A119709.

a(2^n) = 2^n, for all n.

Links

Table of n, a(n) for n=0..72.

Example

9 in binary is 1001. The distinct nonnegative integers that occur as substrings in binary 9 are 0, 1, 2 (10 in binary), 4 (100 in binary), and 9 (1001 in binary). So a(9) = a(0)+a(1)+a(2)+a(4) = 1 + 1 + 2 + 4 = 8.

Crossrefs

Cf. A119709, A165418.

Sequence in context: A223012 A101452 A019963 * A193631 A190993 A326147

Adjacent sequences: A165414 A165415 A165416 * A165418 A165419 A165420

Keyword

base,nonn

Author

Leroy Quet, Sep 17 2009

Extensions

Extended by Ray Chandler, Mar 13 2010

Status

approved