

A240949


Number of partitions of n with the property that if two summands have the same parity, then their frequencies have the same parity.


1



1, 1, 2, 3, 5, 6, 11, 11, 21, 20, 38, 31, 67, 51, 107, 83, 172, 126, 263, 192, 399, 299, 584, 437, 857, 648, 1218, 941, 1743, 1351, 2438, 1912, 3399, 2708, 4672, 3750, 6439, 5193, 8712, 7113, 11815, 9678, 15836, 13056, 21186, 17609, 28080, 23438, 37210, 31181, 48819, 41182, 64039, 54188, 83374, 70923, 108364, 92587
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

The parities of all even parts must be equal and the parities of all odd parts must be equal.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000


EXAMPLE

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.


MATHEMATICA

<<Combinatorica`;
For[n=1, n<=66, n++, Print[]; Print["n= ", n];
p={n};
count=1;
For[k=1, k<=PartitionsP[n]1, k++,
p=NextPartition[p];
tallyp=Tally[p];
condition=True;
For[i=1, i<=Length[tallyp]1, i++,
For[j=i+1, j<=Length[tallyp], j++,
If[(Mod[tallyp[[i]][[1]], 2]==Mod[tallyp[[j]][[1]], 2])&&(Mod[tallyp[[i]][[2]], 2]!= Mod[tallyp[[j]][[2]], 2]), condition=False]]]
If[condition, count++]];
Print[count]];


CROSSREFS

Sequence in context: A164523 A227305 A326612 * A033159 A199366 A332275
Adjacent sequences: A240946 A240947 A240948 * A240950 A240951 A240952


KEYWORD

nonn


AUTHOR

David S. Newman, Aug 04 2014


EXTENSIONS

Terms a(11) and beyond by Joerg Arndt, Aug 04 2014


STATUS

approved



