A118365 -id:A118365 - cp's OEIS frontend

A119268 Number of infinite-dimensional partitions of n up to conjugacy.

1, 1, 1, 2, 4, 7, 14, 28, 58, 120, 260, 571, 1296, 2998, 7124

Offset: 0

Franklin T. Adams-Watters, May 11 2006

Partitions are considered as generalized Ferrers diagrams; any permutation of the axes produces a conjugate. An infinite-dimensional partition thus has infinitely many conjugates. However, an infinite-dimensional partition of n always has a conjugate of dimension at most n-2, so this sequence is always finite.

Cf. A119338, A118364, A118365.

a(n) = A119338(k,n) = A119269(n,k) for any k >= n-2. - Max Alekseyev, Mar 20 2025

More terms from Max Alekseyev, May 16 2006

A119338 Table by antidiagonals: a(m,n) is the number of m-dimensional partitions of n up to conjugacy, for m >= 0, n >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 4, 4, 1, 1, 1, 2, 4, 6, 6, 1, 1, 1, 2, 4, 7, 11, 8, 1, 1, 1, 2, 4, 7, 13, 19, 12, 1, 1, 1, 2, 4, 7, 14, 25, 33, 16, 1, 1, 1, 2, 4, 7, 14, 27, 49, 55, 22, 1, 1, 1, 2, 4, 7, 14, 28, 55, 93, 95, 29, 1, 1, 1, 2, 4, 7, 14, 28, 57, 111, 181, 158, 40, 1

Offset: 1

Max Alekseyev, May 15 2006

Partitions are considered as generalized Ferrers diagrams; any permutation of the axes produces a conjugate.

			Table starts:
  1, 1, 1, 1, 1,  1, ...
  1, 1, 2, 3, 4,  6, ...
  1, 1, 2, 4, 6, 11, ...
  1, 1, 2, 4, 7, 13, ...
  1, 1, 2, 4, 7, 14, ...
  ...

Rows: A000012, A046682, A000786, A119266, A119267, A119340, A119341, A119342 stabilize to A119268. Transposed table is A119269. Cf. A119339, A119270, A118364, A118365.

A118364 Limit of the number of exactly m-dimensional partitions of m+n as m tends to infinity.

Original entry on oeis.org

0, 1, 2, 6, 19, 60

Offset: 1

Max Alekseyev, May 16 2006

Partial sums are given by A118365.

Cf. A119270, A119339, A119268.

a(n)=A119270(m+n,m)=A119339(m+n,n) for all m>=2n-5

cp's OEIS Frontend

A119268 Number of infinite-dimensional partitions of n up to conjugacy.

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A119338 Table by antidiagonals: a(m,n) is the number of m-dimensional partitions of n up to conjugacy, for m >= 0, n >= 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

A118364 Limit of the number of exactly m-dimensional partitions of m+n as m tends to infinity.

Views

Author

Keywords

Comments

Crossrefs

Formula