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A238944 Number of partitions of n that have odd sized Ferrers matrix. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 15:16 EST 2022. Contains 358534 sequences. (Running on oeis4.)