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, 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

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 A366343 A199366

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