A279788 Twice partitioned numbers where the first partition is constant and the latter partitions are strict.

1, 1, 2, 3, 4, 4, 10, 6, 12, 17, 21, 13, 57, 19, 49, 87, 86, 39, 240, 55, 279, 330, 235, 105, 1141, 386, 491, 1217, 1461, 257, 4804, 341, 2968, 4225, 1958, 5898, 18961, 761, 3782, 15007, 30572, 1261, 66245, 1611, 32523, 106951, 13122, 2591, 283013, 81390, 182873

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Gus Wiseman, Sequences enumerating triangles of integer partitions

Example

The a(6)=10 twice-partitions are:
((6)), ((51)), ((42)), ((3)(3)), ((3)(21)), ((21)(3)),
((321)), ((2)(2)(2)), ((21)(21)), ((1)(1)(1)(1)(1)(1)).

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
      `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(b(n/d)^d, d=divisors(n)))
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Dec 20 2016

Mathematica

Table[DivisorSum[n, PartitionsQ[n/#]^#&], {n, 20}]

Crossrefs

Cf. A000005, A000009, A018818, A063834, A279787.

Sequence in context: A202784 A118263 A217478 * A207627 A102539 A240220

Adjacent sequences: A279785 A279786 A279787 * A279789 A279790 A279791

Keyword

nonn

Author

Gus Wiseman, Dec 18 2016

Status

approved