A175359 Let S be the set of positive integers that, when written in binary, exist as substrings in the binary representation of n. a(n) = number of partitions of n into parts that are all members of S. Each part may occur any number of times in a partition.

1, 2, 2, 4, 4, 8, 4, 10, 10, 11, 25, 45, 46, 47, 11, 36, 36, 41, 119, 92, 44, 224, 236, 458, 492, 455, 501, 950, 907, 516, 45, 202, 202, 227, 901, 238, 655, 2188, 2185, 1370, 1382, 265, 1867, 10299, 4103, 7919, 4136, 9676, 10362, 10381, 11238, 26161, 9825

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..4096

Example

6 in binary is 110. The numerical values of the substrings of 110 are 1 (1 in binary), 2 (10 in binary), 3 (11 in binary), and 6 (110 in binary). The partitions of 6 into parts (1,2,3,6) are: 1+1+1+1+1+1, 2+1+1+1+1, 2+2+1+1, 2+2+2, 3+1+1+1, 3+2+1, 3+3, 6. There are 8 such partitions, so a(6) = 8.

Crossrefs

Sequence in context: A115209 A139210 A300123 * A336125 A353125 A330807

Adjacent sequences: A175356 A175357 A175358 * A175360 A175361 A175362

Keyword

base,nonn,look

Author

Leroy Quet, Apr 23 2010

Extensions

More terms from Alois P. Heinz, Oct 13 2011

Status

approved