%I #6 Apr 15 2019 01:38:03
%S 2,3,6,10,18,27,44,64,97,138,200,276,390,528,724,968,1301,1712,2266,
%T 2946,3842,4947,6372,8122,10362,13094,16544,20754,26010,32392,40308,
%U 49876,61648,75845,93178,114006,139308,169586,206158,249814,302267,364664,439330
%N Number of integer partitions (of any nonnegative integer) whose sum minus the lesser of their maximum part and their number of parts is n.
%H Giovanni Resta, <a href="/A325232/b325232.txt">Table of n, a(n) for n = 0..75</a>
%H FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000533">St000533: The maximal number of non-attacking rooks on a Ferrers shape</a>
%F For n > 0, a(n) = Sum_{k > 0} A325227(n + k, k).
%e The a(0) = 1 through a(4) = 18 partitions:
%e () (2) (3) (4) (5)
%e (1) (11) (22) (32) (33)
%e (21) (31) (41) (42)
%e (111) (221) (51)
%e (211) (321) (222)
%e (311) (411) (322)
%e (1111) (331)
%e (2111) (421)
%e (3111) (511)
%e (4111) (2211)
%e (3211)
%e (4211)
%e (5111)
%e (11111)
%e (21111)
%e (31111)
%e (41111)
%e (51111)
%t nn=30;
%t mindif[ptn_]:=If[ptn=={},0,Total[ptn]-Min[Length[ptn],Max[ptn]]];
%t allip=Array[IntegerPartitions,2*nn+2,0,Join];
%t Table[Length[Select[allip,mindif[#]==n&]],{n,0,nn}]
%Y Number of times n appears in A325224.
%Y Cf. A051924, A257541, A263297, A325193, A325194, A325224, A325225, A325227.
%K nonn
%O 0,1
%A _Gus Wiseman_, Apr 13 2019
%E More terms from _Giovanni Resta_, Apr 15 2019