A372542 Total number of modes in all partitions of n.

0, 1, 2, 4, 6, 9, 16, 20, 30, 42, 61, 76, 112, 138, 189, 248, 325, 407, 539, 667, 865, 1083, 1369, 1690, 2140, 2624, 3268, 4009, 4954, 6022, 7417, 8968, 10946, 13218, 16023, 19256, 23264, 27819, 33415, 39873, 47682, 56654, 67527, 79962, 94909, 112130, 132578

Offset

0,3

Comments

Each element of a partition with maximal multiplicity is a mode of this partition.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Formula

a(n) = Sum_{k=0..A003056(n)} k * A362614(n,k).

Example

a(5) = 9 = 1 + 2 + 2 + 1 + 1 + 1 + 1: 5, 32, 41, 221, 311, 2111, 11111.

Maple

b:= proc(n, i, m, t) option remember; `if`(n=0, t, `if`(i<1, 0, add(
      b(n-i*j, i-1, max(j, m), `if`(j>m, 1, `if`(j=m, t+1, t))), j=0..n/i)))
    end:
a:= n-> b(n$2, 0$2):
seq(a(n), n=0..46);

Crossrefs

Cf. A000041, A003056, A362614, A372632.

Sequence in context: A101756 A350552 A352359 * A226007 A372632 A257655

Adjacent sequences: A372539 A372540 A372541 * A372544 A372545 A372546

Keyword

nonn

Author

Alois P. Heinz, May 05 2024

Status

approved