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%I #13 Mar 11 2014 01:32:52
%S 1,2,2,4,4,8,4,10,10,11,25,45,46,47,11,36,36,41,119,92,44,224,236,458,
%T 492,455,501,950,907,516,45,202,202,227,901,238,655,2188,2185,1370,
%U 1382,265,1867,10299,4103,7919,4136,9676,10362,10381,11238,26161,9825
%N 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.
%H Alois P. Heinz, <a href="/A175359/b175359.txt">Table of n, a(n) for n = 1..4096</a>
%e 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.
%K base,nonn,look
%O 1,2
%A _Leroy Quet_, Apr 23 2010
%E More terms from _Alois P. Heinz_, Oct 13 2011
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