A325342 -id:A325342 - cp's OEIS frontend

A325341 Number of partitions p of n such that min(p) <= (number of parts of p) < max(p).

0, 0, 0, 1, 2, 3, 4, 7, 10, 15, 21, 29, 39, 54, 71, 95, 124, 163, 209, 271, 344, 440, 554, 700, 874, 1095, 1357, 1685, 2076, 2559, 3132, 3837, 4671, 5687, 6889, 8343, 10058, 12123, 14552, 17459, 20875, 24941, 29706, 35358, 41966, 49768, 58875, 69587, 82061

Offset: 1

Clark Kimberling, Apr 21 2019

nonn

			a(7) counts these 4 partitions: {6,1}, {5,2}, {5,1,1}, {4,2,1}.

Jason Yuen, Table of n, a(n) for n = 1..10000

Cf. A000041, A003106, A064174, A325340, A325342, A325343.

Table[Count[IntegerPartitions[n], q_ /; Min[q] <= Length[q] < Max[q]], {n, 60}]

a(n) = A000041(n) - A003106(n) - A064174(n). - Jason Yuen, Dec 17 2024

A325343 Number of partitions p of n such that min(p) <= (number of parts of p) <= max(p).

Original entry on oeis.org

1, 0, 1, 2, 3, 4, 7, 9, 14, 19, 27, 36, 50, 65, 87, 114, 149, 192, 249, 316, 404, 510, 643, 805, 1008, 1251, 1553, 1917, 2361, 2895, 3546, 4322, 5262, 6383, 7728, 9330, 11245, 13512, 16213, 19405, 23186, 27643, 32907, 39089, 46366, 54894, 64893, 76584, 90256

Offset: 1

Clark Kimberling, Apr 21 2019

nonn

			a(7) counts these 7 partitions: {6,1}, {5,2}, {5,1,1}, {4,2,1}, {4,1,1,1}, {3,3,1}, {3,2,2}.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000041, A003106, A064173, A325340, A325341, A325342.

Table[Count[IntegerPartitions[n], q_ /; Min[q] <= Length[q] <= Max[q]], {n, 60}]

a(n) = A000041(n) - A003106(n) - A064173(n) for n > 0. - Jason Yuen, Dec 15 2024

A325340 Number of partitions p of n such that min(p) < (number of parts of p) < max(p).

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 3, 6, 9, 13, 18, 26, 35, 50, 66, 90, 117, 155, 199, 260, 331, 425, 537, 681, 852, 1070, 1328, 1652, 2038, 2517, 3083, 3783, 4609, 5618, 6811, 8257, 9959, 12014, 14429, 17322, 20721, 24771, 29515, 35147, 41730, 49507, 58585, 69267, 81705

Offset: 1

Clark Kimberling, Apr 21 2019

			a(7) counts these 3 partitions: {6,1}, {5,1,1}, {4,2,1}.

Cf. A000041, A325341, A325342, A325343.

Table[Count[IntegerPartitions[n], q_ /; Min[q] < Length[q] < Max[q]], {n, 60}]

cp's OEIS Frontend

A325341 Number of partitions p of n such that min(p) <= (number of parts of p) < max(p).

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A325343 Number of partitions p of n such that min(p) <= (number of parts of p) <= max(p).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A325340 Number of partitions p of n such that min(p) < (number of parts of p) < max(p).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica