cp's OEIS Frontend

A238945 Number of partitions of n that have even-sized Ferrers matrix.

%I A238945 #8 Apr 07 2020 21:34:21
%S A238945 1,0,2,2,5,5,8,9,16,19,30,37,54,66,91,112,152,187,248,307,401,495,635,
%T A238945 781,990,1210,1517,1849,2296,2788,3434,4155,5087,6132,7460,8963,10844,
%U A238945 12980,15624,18638,22332,26553
%N A238945 Number of partitions of n that have even-sized Ferrers matrix.
%C A238945 Also, the number of even 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 A238945 a(n) + A238944(n) = A000041(n).
%e A238945 (See the example at A238943.)
%t A238945 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 A238945 u = Table[Count[t[[n]], 0], {n, 1, z}]  (* A238944 *)
%t A238945 v = Table[Count[t[[n]], 1], {n, 1, z}]  (* A238945 *)
%Y A238945 Cf. A237981, A238944, A238943, A000041.
%K A238945 nonn,easy
%O A238945 1,3
%A A238945 _Clark Kimberling_, Mar 07 2014