A332706 Index position of {2}^n within the list of partitions of 2n in canonical ordering.

1, 1, 3, 8, 18, 37, 71, 128, 223, 376, 617, 991, 1563, 2423, 3704, 5589, 8333, 12293, 17959, 25996, 37318, 53153, 75153, 105535, 147249, 204201, 281563, 386128, 526795, 715191, 966437, 1300125, 1741598, 2323487, 3087701, 4087933, 5392747, 7089463, 9289053

Offset: 0

Author

Alois P. Heinz, Feb 20 2020

Keywords

• nonn

Comments

The canonical ordering of partitions is described in A080577.

Examples

			a(3) = 8, because 222 has position 8 within the list of partitions of 6 in canonical ordering: 6, 51, 42, 411, 33, 321, 3111, 222, ... .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000

Crossrefs

Bisection (even part) of A058984.

Cf. A000041, A080577, A216053, A238639, A238640, A322761, A330661.

Programs

Maple

a:= n-> combinat[numbpart](2*n)-n:
seq(a(n), n=0..44);

Mathematica

a[n_] := PartitionsP[2n] - n;
Table[a[n], {n, 0, 44}] (* Jean-François Alcover, Aug 20 2021, from Maple *)

Formula

a(n) = A000041(2n) - n.

a(n) = A058984(2n).

a(n) = A330661(2n,n).