A119338 -id:A119338

A119268

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

+10
9

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

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.

LINKS

Table of n, a(n) for n=0..14.

CROSSREFS

Cf. A119338, A118364, A118365.

KEYWORD

more,nonn

AUTHOR

Franklin T. Adams-Watters, May 11 2006

EXTENSIONS

More terms from Max Alekseyev, May 16 2006

STATUS

approved

A119269

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

+10
9

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,8

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

LINKS

Table of n, a(n) for n=1..91.

FORMULA

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

EXAMPLE

Table starts:

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.

KEYWORD

nonn,tabl

AUTHOR

Franklin T. Adams-Watters, May 11 2006

EXTENSIONS

More terms from Max Alekseyev, May 14 2006

STATUS

approved

A119266

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

+10
6

1, 1, 1, 2, 4, 7, 13, 25, 49, 93, 181, 351, 687, 1332, 2591, 5003, 9644, 18462, 35208, 66721, 125840, 235914, 440020, 816122

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..23.

CROSSREFS

Cf. A119269, A000293.

Cf. A119338.

KEYWORD

more,nonn

AUTHOR

Franklin T. Adams-Watters, May 11 2006

EXTENSIONS

More terms from Max Alekseyev, May 15 2006

STATUS

approved

A119267

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

+10
5

1, 1, 1, 2, 4, 7, 14, 27, 55, 111, 232, 486, 1039, 2226, 4820, 10449, 22727, 49354, 107117, 231774, 500040

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..20.

CROSSREFS

Cf. A119269, A000334.

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

KEYWORD

more,nonn

AUTHOR

Franklin T. Adams-Watters, May 11 2006

EXTENSIONS

More terms from Max Alekseyev, May 16 2006

STATUS

approved

A119340

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

+10
5

1, 1, 1, 2, 4, 7, 14, 28, 57, 117, 251, 543, 1209, 2724, 6251, 14505, 34055, 80450

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..17.

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Max Alekseyev, May 16 2006

STATUS

approved

A119341

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

+10
5

1, 1, 1, 2, 4, 7, 14, 28, 58, 119, 257, 562, 1268, 2910, 6844, 16371

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..15.

CROSSREFS

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

KEYWORD

more,nonn

AUTHOR

Max Alekseyev, May 16 2006

STATUS

approved

A119342

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

+10
5

1, 1, 1, 2, 4, 7, 14, 28, 58, 120, 259, 568, 1287, 2970, 7036

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..14.

CROSSREFS

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

KEYWORD

more,nonn

AUTHOR

Max Alekseyev, May 16 2006

STATUS

approved

A119339

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

+10
4

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,8

LINKS

Table of n, a(n) for n=0..84.

EXAMPLE

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.

KEYWORD

nonn,tabl

AUTHOR

Max Alekseyev, May 15 2006

STATUS

approved

A118365

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

+10
3

0, 1, 3, 9, 28, 88

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

LINKS

Table of n, a(n) for n=2..7.

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.

CROSSREFS

Cf. A119269, A119338, A119268.

KEYWORD

hard,more,nonn

AUTHOR

Max Alekseyev, May 17 2006

STATUS

approved