A208571 Number of non-practical binary partitions of n.

0, 1, 0, 2, 1, 3, 0, 4, 2, 6, 2, 8, 5, 11, 0, 10, 4, 14, 4, 18, 10, 24, 6, 26, 14, 34, 16, 42, 27, 53, 0, 36, 10, 46, 8, 54, 22, 68, 12, 72, 30, 90, 32, 106, 56, 130, 26, 120, 52, 146, 54, 168, 88, 202, 80, 220, 122, 262, 134, 300, 187, 353, 0, 202, 36, 238, 20, 258, 66, 304, 24, 308, 78, 362, 68, 398, 136, 466, 52, 442, 124, 514, 112, 562, 202, 652, 160, 684, 266, 790, 272, 870, 402, 1000, 166, 858, 286, 978, 270, 1056

Offset

1,4

Comments

A practical partition is one in which 1..n can all be represented as a sum of a subset of the members of the partition.

Links

Table of n, a(n) for n=1..100.

J. Dixmier and J. L. Nicolas, Partitions without small parts, Colloquia Mathematica Societatis Janos Bolyai 51, Number Theory, Budapest, Hungary, 1987, pp. 9-33.

P. Erdos and J. L. Nicolas, On practical partitions, Collectanea Mathematica 46:1-2 (1995), pp. 57-76.

P. Erdos and M. Szalay, On some problems of J. Denes and P. Turan, Studies in Pure Mathematics to the memory of P. Turan, Editor P. Erdos, Budapest 1983, pp. 187-212.

Example

The binary partitions of 4 are 4, 2+2, 2+1+1, and 1+1+1+1; 4 and 2+2 cannot represent 1, but the other two represent all of 1, 2, 3, and 4. Thus a(4) = 2.

Crossrefs

Cf. A018819.

Sequence in context: A025480 A088002 A030109 * A264520 A058208 A070817

Adjacent sequences: A208568 A208569 A208570 * A208572 A208573 A208574

Keyword

nonn

Author

Charles R Greathouse IV, Mar 20 2012

Status

approved