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

0, 2, 1, 3, 2, 6, 7, 13, 14, 23, 26, 40, 47, 69, 85, 119, 145, 198, 242, 320, 391, 507, 620, 794, 968, 1226, 1493, 1869, 2269, 2816, 3408, 4194, 5056, 6178, 7423, 9014, 10793, 13035, 15561, 18700, 22251, 26621

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..42.

Formula

a(n) + A238945(n) = A000041(n).

Example

(See the example at A238943.)

Mathematica

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];
u = Table[Count[t[[n]], 0], {n, 1, z}]  (* A238944 *)
v = Table[Count[t[[n]], 1], {n, 1, z}]  (* A238945 *)

Crossrefs

Cf. A237981, A238945, A238943, A000041.

Sequence in context: A335688 A206494 A022477 * A144238 A319622 A348747

Adjacent sequences: A238941 A238942 A238943 * A238945 A238946 A238947

Keyword

nonn,easy

Author

Clark Kimberling, Mar 07 2014

Status

approved