A344680 Number of partitions of n that are also multiplicity multiset of a partition of 2n.

1, 1, 2, 3, 4, 4, 8, 8, 12, 14, 18, 21, 30, 33, 41, 49, 62, 70, 86, 98, 116, 133, 160, 181, 214, 237, 282, 311, 364, 407, 466, 522, 600, 652, 761, 815, 937, 1038, 1179, 1271, 1442, 1577, 1762, 1930, 2158, 2311, 2636, 2831, 3146, 3402, 3784, 4057, 4537, 4869, 5365, 5745, 6370, 6802, 7562, 8061, 8785, 9471, 10410

Offset

0,3

Links

Table of n, a(n) for n=0..62.

Formula

a(n) = A337584(2n,n).

Example

a(0) = 1: [].
a(1) = 1: [1].
a(2) = 2: [2], [1,1].
a(3) = 3: [3], [1,2], [1,1,1].
a(4) = 4: [4], [1,3], [2,2], [1,1,2].
a(5) = 4: [5], [1,4], [1,1,3], [1,2,2].
a(6) = 8: [6], [1,5], [2,4], [3,3], [1,1,4], [1,2,3], [2,2,2], [1,1,1,3].
a(7) = 8: [7], [1,6], [1,1,5], [1,2,4], [1,3,3], [2,2,3], [1,1,1,4], [1,1,2,3].

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, `if`(n=0, {[]}, {[n]}),
     {b(n, i-1)[], seq(map(x-> sort([x[], j]), b(n-i*j, i-1))[], j=1..n/i)})
    end:
a:= n-> nops(select(l-> add(i, i=l)=n, b(2*n$2))):
seq(a(n), n=0..30);

Crossrefs

Cf. A088887, A337584.

Sequence in context: A319079 A325329 A224038 * A330147 A241037 A097093

Adjacent sequences: A344677 A344678 A344679 * A344681 A344682 A344683

Keyword

nonn

Author

Alois P. Heinz, Aug 17 2021

Status

approved