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

0,3

Comments

The canonical ordering of partitions is described in A080577.

Links

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

Formula

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

a(n) = A058984(2n).

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

Example

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, ... .

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 *)

Crossrefs

Bisection (even part) of A058984.

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

Sequence in context: A227161 A241080 A366724 * A000234 A136376 A099845

Adjacent sequences: A332703 A332704 A332705 * A332707 A332708 A332709

Keyword

nonn

Author

Alois P. Heinz, Feb 20 2020

Status

approved