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%I #21 Aug 17 2014 16:53:59
%S 1,1,2,3,5,6,11,11,21,20,38,31,67,51,107,83,172,126,263,192,399,299,
%T 584,437,857,648,1218,941,1743,1351,2438,1912,3399,2708,4672,3750,
%U 6439,5193,8712,7113,11815,9678,15836,13056,21186,17609,28080,23438,37210,31181,48819,41182,64039,54188,83374,70923,108364,92587
%N Number of partitions of n with the property that if two summands have the same parity, then their frequencies have the same parity.
%C The parities of all even parts must be equal and the parities of all odd parts must be equal.
%H Alois P. Heinz, <a href="/A240949/b240949.txt">Table of n, a(n) for n = 0..1000</a>
%e For example: for n=5 the partition 3,1,1 is not counted, because 3 and 1 have the same parity, but the frequency of 3 and the frequency of 1 have different parity.
%t <<Combinatorica`;
%t For[n=1,n<=66,n++,Print[];Print["n= ",n];
%t p={n};
%t count=1;
%t For[k=1,k<=PartitionsP[n]-1,k++,
%t p=NextPartition[p];
%t tallyp=Tally[p];
%t condition=True;
%t For[i=1,i<=Length[tallyp]-1,i++,
%t For[j=i+1,j<=Length[tallyp],j++,
%t If[(Mod[tallyp[[i]][[1]],2]==Mod[tallyp[[j]][[1]],2])&&(Mod[tallyp[[i]][[2]],2]!= Mod[tallyp[[j]][[2]],2]),condition=False]]]
%t If[condition,count++]];
%t Print[count]];
%K nonn
%O 0,3
%A _David S. Newman_, Aug 04 2014
%E Terms a(11) and beyond by _Joerg Arndt_, Aug 04 2014
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