

A208571


Number of nonpractical binary partitions of n.


0



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
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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. 933.
P. Erdos and J. L. Nicolas, On practical partitions, Collectanea Mathematica 46:12 (1995), pp. 5776.
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. 187212.


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



