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 A208571 Number of non-practical binary partitions of n. 0

%I

%S 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,

%T 27,53,0,36,10,46,8,54,22,68,12,72,30,90,32,106,56,130,26,120,52,146,

%U 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

%N Number of non-practical binary partitions of n.

%C 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.

%H J. Dixmier and J. L. Nicolas, <a href="http://math.univ-lyon1.fr/~nicolas/dixmiersmallparts.pdf">Partitions without small parts</a>, Colloquia Mathematica Societatis Janos Bolyai 51, Number Theory, Budapest, Hungary, 1987, pp. 9-33.

%H P. Erdos and J. L. Nicolas, <a href="http://www.collectanea.ub.edu/index.php/Collectanea/article/view/3814/4518">On practical partitions</a>, Collectanea Mathematica 46:1-2 (1995), pp. 57-76.

%H P. Erdos and M. Szalay, <a href="http://www.renyi.hu/~p_erdos/1983-16.pdf">On some problems of J. Denes and P. Turan</a>, Studies in Pure Mathematics to the memory of P. Turan, Editor P. Erdos, Budapest 1983, pp. 187-212.

%e 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.

%Y Cf. A018819.

%K nonn

%O 1,4

%A _Charles R Greathouse IV_, Mar 20 2012

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