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A238945 Number of partitions of n that have even-sized Ferrers matrix. 3
1, 0, 2, 2, 5, 5, 8, 9, 16, 19, 30, 37, 54, 66, 91, 112, 152, 187, 248, 307, 401, 495, 635, 781, 990, 1210, 1517, 1849, 2296, 2788, 3434, 4155, 5087, 6132, 7460, 8963, 10844, 12980, 15624, 18638, 22332, 26553 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

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

FORMULA

a(n) + A238944(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, A238944, A238943, A000041.

Sequence in context: A168236 A035624 A073707 * A091609 A183563 A222706

Adjacent sequences:  A238942 A238943 A238944 * A238946 A238947 A238948

KEYWORD

nonn,easy,changed

AUTHOR

Clark Kimberling, Mar 07 2014

STATUS

approved

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Last modified April 8 04:26 EDT 2020. Contains 333312 sequences. (Running on oeis4.)