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

Author

Alford Arnold, May 25 2009, Jun 20 2009

Keywords

• easy
• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A053445, A160644.

Programs

Mathematica

Join[{0},Differences[Take[Differences[Table[PartitionsP[n],{n,0,100}],2],{2,-1,2}]]] (* Harvey P. Dale, Sep 02 2013 *)

Extensions

Extended and edited by Nathaniel Johnston, Apr 30 2011