A328863 Number of partitions of 2n that describe the degree sequence of exactly one labeled multigraph with no loops.

1, 2, 4, 6, 9, 14, 19, 27, 37, 50, 66, 89, 115, 151, 195, 252, 321, 412, 520, 660, 829, 1042, 1299, 1623, 2010, 2492, 3071, 3783, 4635, 5679, 6922, 8434, 10234, 12406, 14985, 18085, 21751, 26135, 31312, 37471, 44723, 53321, 63415, 75336, 89303, 105734, 124938

Offset

1,2

Comments

Also the number of partitions of 2*n either with largest part equal to n or with three parts and largest part less than n.

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000041(n) + A069905(n).

Example

For n = 4, the a(4) = 6 partitions of 2*4 = 8 that describe a degree sequence of exactly one labeled multigraph are
  4 + 4,
  4 + 3 + 1,
  4 + 2 + 2,
  4 + 2 + 1 + 1,
  4 + 1 + 1 + 1 + 1, and
  3 + 3 + 2.

Crossrefs

Cf. A000041, A069905, A209816.

Sequence in context: A117842 A067588 A003402 * A218004 A346634 A034748

Adjacent sequences: A328860 A328861 A328862 * A328864 A328865 A328866

Keyword

nonn

Author

Peter Kagey, Oct 28 2019

Status

approved