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

Author

Alois P. Heinz, Aug 17 2021

Keywords

• nonn

Examples

			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].
		

Crossrefs

Cf. A088887, A337584.

Programs

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);

Formula

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