login
A160643
Bisect A053445 then calculate the first differences of the resulting sequence.
4
0, 0, 0, 1, 1, 1, 4, 4, 6, 11, 15, 20, 33, 43, 60, 88, 119, 160, 226, 300, 404, 549, 727, 961, 1283, 1680, 2201, 2887, 3750, 4857, 6301, 8105, 10410, 13357, 17050, 21714, 27625, 34992, 44240, 55840, 70261, 88220, 110600, 138274, 172558, 214984, 267234
OFFSET
1,7
COMMENTS
a(n) counts the following subset of the partitions (cf. A000041): the number being partitioned is odd, the minimum part is two
and the three largest parts match.
First differences of A161921.
LINKS
EXAMPLE
A161921 begins: 0, 0, 1, 2, 3, 7, 11, 17, 28, 43, 63, 96, 139, 199, 287, 406, 566, ...
Therefore a(n) begins 0, 0, 0, 1, 1, 1, 4, 4, 6, ..., counting 333; 3332; 33322; 555, 4443, 333222, 33333; etc.
MATHEMATICA
Join[{0}, Differences[Take[Differences[Table[PartitionsP[n], {n, 0, 100}], 2], {2, -1, 2}]]] (* Harvey P. Dale, Sep 02 2013 *)
CROSSREFS
Sequence in context: A213425 A213426 A054223 * A078321 A195954 A278532
KEYWORD
easy,nonn
AUTHOR
Alford Arnold, May 25 2009, Jun 20 2009
EXTENSIONS
Extended and edited by Nathaniel Johnston, Apr 30 2011
STATUS
approved