cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A119266 Number of 3-dimensional partitions of n up to conjugacy.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 13, 25, 49, 93, 181, 351, 687, 1332, 2591, 5003, 9644, 18462, 35208, 66721, 125840, 235914, 440020, 816122, 1505986, 2764303, 5048960, 9176069
Offset: 0

Views

Author

Franklin T. Adams-Watters, May 11 2006

Keywords

Comments

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

Crossrefs

Cf. A119269, A000293.
Cf. A119338.
Cf. A096573, A096575, A382247, A096577

Formula

a(n) = (A000293(n) + 6*A096573(n) + 8*A096575(n) + 3*A382247(n) + 6*A096577(n))/24 by Burnside's lemma. - Wouter Meeussen, Mar 19 2025

Extensions

a(9)-a(23) from Max Alekseyev, May 15 2006
a(24)-a(27) from Max Alekseyev, Mar 20 2025

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

Original entry on oeis.org

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

Views

Author

Franklin T. Adams-Watters, May 11 2006

Keywords

Comments

Partitions are considered as generalized Ferrers diagrams; any permutation of the axes produces a conjugate.
Transposed table is A119338. - Max Alekseyev, May 14 2006

Examples

			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

Crossrefs

Columns A005987, A000786, A119266, A119267; diagonal A119268. Cf. A096751, A119270.
Cf. A119339, A119340, A119341, A119342.

Formula

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

Extensions

More terms from Max Alekseyev, May 14 2006

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

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 14, 28, 58, 120, 260, 571, 1296, 2998, 7124
Offset: 0

Views

Author

Franklin T. Adams-Watters, May 11 2006

Keywords

Comments

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.

Crossrefs

Cf. A119338, A118364, A118365.

Formula

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

Extensions

More terms from Max Alekseyev, May 16 2006

A119267 Number of 4-dimensional partitions of n up to conjugacy.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 14, 27, 55, 111, 232, 486, 1039, 2226, 4820, 10449, 22727, 49354, 107117, 231774, 500040, 1074476, 2299589, 4899650
Offset: 0

Views

Author

Franklin T. Adams-Watters, May 11 2006

Keywords

Comments

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

Crossrefs

Cf. A119269, A000334.
Cf. A119266, A119338, A119340, A119341, A119342.

Extensions

a(9)-a(20) from Max Alekseyev, May 16 2006
a(21)-a(23) from Max Alekseyev, Mar 20 2025

A119340 Number of 5-dimensional partitions of n up to conjugacy.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 14, 28, 57, 117, 251, 543, 1209, 2724, 6251, 14505, 34055, 80450, 191166, 455473, 1086863, 2592817
Offset: 0

Views

Author

Max Alekseyev, May 16 2006

Keywords

Comments

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

Crossrefs

Cf. A000390, A119266, A119267, A119268, A119269, A119338, A119341, A119342.

Extensions

a(18)-a(21) from Max Alekseyev, Mar 30 2025

A119341 Number of 6-dimensional partitions of n up to conjugacy.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 14, 28, 58, 119, 257, 562, 1268, 2910, 6844, 16371, 39910, 98667, 247200, 625559
Offset: 0

Views

Author

Max Alekseyev, May 16 2006

Keywords

Comments

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

Crossrefs

Cf. A000416, A119266, A119267, A119268, A119269, A119338, A119340, A119342.

Extensions

a(16)-a(19) from Max Alekseyev, Mar 31 2025

A119342 Number of 7-dimensional partitions of n up to conjugacy.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 14, 28, 58, 120, 259, 568, 1287, 2970, 7036, 17009, 42042, 105848
Offset: 0

Views

Author

Max Alekseyev, May 16 2006

Keywords

Comments

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

Crossrefs

Cf. A000427, A119266, A119267, A119268, A119269, A119338, A119340, A119341.

Extensions

a(15)-a(17) from Max Alekseyev, Apr 02 2025

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

Views

Author

Max Alekseyev, May 15 2006

Keywords

Examples

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

Crossrefs

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

Views

Author

Max Alekseyev, May 17 2006

Keywords

Crossrefs

Cf. A119269, A119338, A119268.

Formula

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.
Showing 1-9 of 9 results.

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