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A238944 Number of partitions of n that have odd sized Ferrers matrix.

%I A238944 #7 Apr 06 2020 22:16:43
%S A238944 0,2,1,3,2,6,7,13,14,23,26,40,47,69,85,119,145,198,242,320,391,507,
%T A238944 620,794,968,1226,1493,1869,2269,2816,3408,4194,5056,6178,7423,9014,
%U A238944 10793,13035,15561,18700,22251,26621
%N A238944 Number of partitions of n that have odd sized Ferrers matrix.
%C A238944 Also, the number of odd numbers in row n of the array at A238943.  Suppose that p is a partition of n, and let m = max{greatest part of p, number of parts of p}.  Write the Ferrers graph of p with 1's as nodes, and pad the graph with 0's to form an m X m square matrix, which is introduced at A237981 as the Ferrers matrix of p, denoted by f(p).  The size of f(p) is m.
%F A238944 a(n) + A238945(n) = A000041(n).
%e A238944 (See the example at A238943.)
%t A238944 p[n_, k_] := p[n, k] = IntegerPartitions[n][[k]]; a[t_] := Max[Max[t], Length[t]]; z = 42; t = Mod[Table[a[p[n, k]], {n, 1, z}, {k, 1, PartitionsP[n]}], 2];
%t A238944 u = Table[Count[t[[n]], 0], {n, 1, z}]  (* A238944 *)
%t A238944 v = Table[Count[t[[n]], 1], {n, 1, z}]  (* A238945 *)
%Y A238944 Cf. A237981, A238945, A238943, A000041.
%K A238944 nonn,easy
%O A238944 1,2
%A A238944 _Clark Kimberling_, Mar 07 2014