A118364 -id:A118364 - 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.

A119270 Triangle: number of exactly (m-1)-dimensional partitions of n, up to conjugacy, for n >= 1, m >= 0.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 1, 5, 5, 2, 1, 0, 1, 7, 11, 6, 2, 1, 0, 1, 11, 21, 16, 6, 2, 1, 0, 1, 15, 39, 38, 18, 6, 2, 1, 0, 1, 21, 73, 86, 51, 19, 6, 2, 1, 0, 1, 28, 129, 193, 135, 57, 19, 6, 2, 1, 0, 1, 39, 227, 420, 352, 170, 59, 19, 6, 2, 1, 0, 1, 51, 390, 890, 894

Offset: 1

Franklin T. Adams-Watters, May 11 2006

The partition of 1 is considered to be dimension -1 by convention.

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

			Table starts:
1
0,1
0,1,1
0,1,2,1
0,1,3,2,1

Cf. A119269, A119271.

Reversed triangle is A119339. Columns stabilize to A118364.

a(n,m) = A119269(n,m)-A119269(n,m-1).

More terms from Max Alekseyev, May 15 2006

A119339 Triangle: number of exactly (m-1)-dimensional partitions of n, up to conjugacy, for n >= 1, m=n..1.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 3, 1, 0, 1, 2, 5, 5, 1, 0, 1, 2, 6, 11, 7, 1, 0, 1, 2, 6, 16, 21, 11, 1, 0, 1, 2, 6, 18, 38, 39, 15, 1, 0, 1, 2, 6, 19, 51, 86, 73, 21, 1, 0, 1, 2, 6, 19, 57, 135, 193, 129, 28, 1, 0, 1, 2, 6, 19, 59, 170, 352, 420, 227, 39, 1, 0, 1, 2, 6, 19, 60, 186, 498

Offset: 0

Max Alekseyev, May 15 2006

			Table starts:
1
1,0
1,1,0
1,2,1,0
1,2,3,1,0

Reversed triangle is A119270. Diagonals stabilize to A118364. Cf. A119269, A119338.

A118365 Limiting difference of the number of infinity-dimensional partitions and m-dimensional partitions of m+n as m tends to infinity.

Original entry on oeis.org

0, 1, 3, 9, 28, 88

Offset: 2

Max Alekseyev, May 17 2006

Cf. A119269, A119338, A119268.

a(n)=A119268(m+n)-A119269(m+n,m)=A119268(m+n)-A119338(m,m+n) for all m>=2n-8. Partial sums of A118364.

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.

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Examples

Crossrefs

A119270 Triangle: number of exactly (m-1)-dimensional partitions of n, up to conjugacy, for n >= 1, m >= 0.

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Author

Keywords

Comments

Examples

Crossrefs

Formula

Extensions

A119339 Triangle: number of exactly (m-1)-dimensional partitions of n, up to conjugacy, for n >= 1, m=n..1.

Views

Author

Keywords

Examples

Crossrefs

A118365 Limiting difference of the number of infinity-dimensional partitions and m-dimensional partitions of m+n as m tends to infinity.

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Author

Keywords

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Formula