A160643 - OEIS

%I #7 Sep 02 2013 14:46:06

%S 0,0,0,1,1,1,4,4,6,11,15,20,33,43,60,88,119,160,226,300,404,549,727,

%T 961,1283,1680,2201,2887,3750,4857,6301,8105,10410,13357,17050,21714,

%U 27625,34992,44240,55840,70261,88220,110600,138274,172558,214984,267234

%N Bisect A053445 then calculate the first differences of the resulting sequence.

%C a(n) counts the following subset of the partitions (cf. A000041): the number being partitioned is odd, the minimum part is two

%C and the three largest parts match.

%C First differences of A161921.

%H Nathaniel Johnston, <a href="/A160643/b160643.txt">Table of n, a(n) for n = 1..2500</a>

%e A161921 begins: 0, 0, 1, 2, 3, 7, 11, 17, 28, 43, 63, 96, 139, 199, 287, 406, 566, ...

%e Therefore a(n) begins 0, 0, 0, 1, 1, 1, 4, 4, 6, ..., counting 333; 3332; 33322; 555, 4443, 333222, 33333; etc.

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

%Y Cf. A053445, A160644.

%K easy,nonn

%O 1,7

%A _Alford Arnold_, May 25 2009, Jun 20 2009

%E Extended and edited by _Nathaniel Johnston_, Apr 30 2011