A255834 -id:A255834

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A219555

Number of bipartite partitions of (i,j) with i+j = n into distinct pairs.

+10
15

1, 2, 4, 10, 19, 38, 73, 134, 242, 430, 749, 1282, 2171, 3622, 5979, 9770, 15802, 25334, 40288, 63560, 99554, 154884, 239397, 367800, 561846, 853584, 1290107, 1940304, 2904447, 4328184, 6422164, 9489940, 13967783, 20480534, 29920277, 43557272, 63194864

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

CROSSREFS

Cf. A026007, A052812, A005380, A255834, A255836.

A255835

G.f.: Product_{k>=1} (1+x^k)^(2*k-1).

+10
11

1, 1, 3, 8, 15, 34, 67, 133, 255, 486, 901, 1649, 2984, 5312, 9373, 16342, 28221, 48283, 81928, 137858, 230278, 381919, 629156, 1029933, 1675856, 2711288, 4362575, 6983196, 11122327, 17630798, 27820283, 43706461, 68375137, 106534093, 165340844, 255643289

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

CROSSREFS

Cf. A026007, A219555, A052812, A253289, A255834.

A052812

A simple grammar: power set of pairs of sequences.

+10
10

1, 0, 1, 2, 3, 6, 9, 16, 24, 42, 63, 102, 157, 244, 373, 570, 858, 1290, 1930, 2858, 4228, 6208, 9084, 13216, 19175, 27666, 39804, 57020, 81412, 115820, 164264, 232178, 327220, 459796, 644232, 900214, 1254554, 1743896, 2418071, 3344896, 4616026

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

CROSSREFS

Cf. A026007, A052847, A219555, A255834, A255835.

A120844

Number of multi-trace BPS operators for the quiver gauge theory of the orbifold C^2/Z_2.

+10
6

1, 3, 11, 32, 90, 231, 576, 1363, 3141, 7003, 15261, 32468, 67788, 138892, 280103, 556302, 1089991, 2108332, 4030649, 7620671, 14261450, 26431346, 48544170, 88393064, 159654022, 286149924, 509137464, 899603036, 1579014769

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

CROSSREFS

Cf. A005380, A253289, A255271, A255802, A255834.

A255836

G.f.: Product_{k>=1} (1+x^k)^(3*k+1).

+10
5

1, 4, 13, 42, 117, 310, 785, 1896, 4433, 10062, 22248, 48080, 101821, 211682, 432795, 871520, 1730491, 3391894, 6568996, 12580316, 23841774, 44742634, 83193865, 153347110, 280336704, 508499474, 915540681, 1636805438, 2906642396, 5128530946, 8993376689

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

CROSSREFS

Cf. A026007, A219555, A052812, A255271, A255834, A255835, A255837.

A255837

G.f.: Product_{k>=1} (1+x^k)^(3*k+2).

+10
3

1, 5, 18, 61, 182, 506, 1338, 3369, 8172, 19197, 43833, 97636, 212748, 454461, 953505, 1968095, 4001627, 8024295, 15885484, 31074351, 60111277, 115071431, 218126868, 409662895, 762679151, 1408172844, 2579599582, 4690277001, 8467363674, 15182486586

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

CROSSREFS

Cf. A026007 (k), A219555 (k+1), A052812 (k-1), A255834 (2*k+1), A255835 (2*k-1), A255836 (3*k+1).

A363600

Number of partitions of n into distinct parts where there are k^2+1 kinds of part k.

+10
1

1, 2, 6, 20, 52, 140, 356, 880, 2123, 5016, 11610, 26400, 59130, 130476, 284216, 611592, 1301344, 2740194, 5713930, 11806144, 24184908, 49142504, 99091244, 198360536, 394342884, 778818658, 1528531702, 2982017956, 5784365082, 11158728448, 21413292868

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

CROSSREFS

Cf. A027998, A219555, A255834, A363599.

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