A160643 Bisect A053445 then calculate the first differences of the resulting sequence.

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

Nathaniel Johnston, Table of n, a(n) for n = 1..2500

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

Cf. A053445, A160644.

Sequence in context: A213425 A213426 A054223 * A078321 A195954 A278532

Adjacent sequences: A160640 A160641 A160642 * A160644 A160645 A160646

Keyword

easy,nonn

Author

Alford Arnold, May 25 2009, Jun 20 2009

Extensions

Extended and edited by Nathaniel Johnston, Apr 30 2011

Status

approved