A119339 -id:A119339 - cp's OEIS frontend

A119269 Table by antidiagonals: number of m-dimensional partitions of n up to conjugacy, for n >= 1, m >= 0.

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

Offset: 1

Franklin T. Adams-Watters, May 11 2006

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

Transposed table is A119338. - Max Alekseyev, May 14 2006

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

Columns A005987, A000786, A119266, A119267; diagonal A119268. Cf. A096751, A119270.

Cf. A119339, A119340, A119341, A119342.

a(n,m) = a(n,n-2) for m >= n-1.

More terms from Max Alekseyev, May 14 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

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

cp's OEIS Frontend

A119269 Table by antidiagonals: number of m-dimensional partitions of n up to conjugacy, for n >= 1, m >= 0.

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

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Author

Keywords

Comments

Crossrefs

Formula

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

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Author

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Formula

Extensions