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%I #8 Feb 16 2025 08:32:51
%S 1,2,3,5,6,10,13,19,24,33,41,56,68,90,111,143,172,219,263,328,392,483,
%T 573,700,823,993,1166,1396,1626,1936,2249,2655,3070,3603,4151,4848,
%U 5562,6461,7395,8548,9741,11219,12754,14624,16578,18943,21415,24388
%N Number of partitions of n into numbers having in binary representation at most trailing zeros.
%C a(n) <= A000041(n), a(n) < A000041(n) for n >= 5 -> '101'.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Partition.html">Partition</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>
%e n=8, the 8th partition number is 22: three (5+3, 5+2+1 and 5+1+1+1) do not count, as 5 = '101', therefore a(8)=19.
%Y Cf. A023758, A007088.
%K nonn,changed
%O 1,2
%A _Reinhard Zumkeller_, Oct 02 2003