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A328863 Number of partitions of 2n that describe the degree sequence of exactly one labeled multigraph with no loops. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A034748 A069916

Adjacent sequences:  A328860 A328861 A328862 * A328864 A328865 A328866

KEYWORD

nonn

AUTHOR

Peter Kagey, Oct 28 2019

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)