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 1-8 of 8 results.

A347587 Number of partitions of n into at most 5 distinct parts.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 75, 88, 102, 119, 137, 158, 181, 207, 235, 268, 302, 341, 383, 430, 480, 536, 595, 661, 731, 808, 889, 979, 1073, 1176, 1285, 1403, 1527, 1662, 1803, 1956, 2116, 2288, 2468, 2662, 2864, 3080, 3306, 3547
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 08 2021

Keywords

Links

Crossrefs

Cf. A001401, A014591, A065033, A347586, A347588.

Programs

  • Mathematica
    nmax = 58; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 5}], {x, 0, nmax}], x]
LinearRecurrence[{1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, -1, -1, 1}, {1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22}, 59]

Formula

G.f.: Sum_{k=0..5} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

A347588 Number of partitions of n into at most 6 distinct parts.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76, 89, 104, 122, 142, 165, 192, 221, 255, 294, 337, 385, 441, 501, 570, 646, 731, 824, 930, 1043, 1171, 1310, 1464, 1630, 1817, 2015, 2236, 2473, 2734, 3013, 3322, 3648, 4008, 4391, 4809, 5252, 5738, 6249
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 08 2021

Keywords

Links

Crossrefs

Cf. A001402, A014591, A065033, A347586, A347587.

Programs

  • Mathematica
    nmax = 58; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 6}], {x, 0, nmax}], x]
Join[{1}, LinearRecurrence[{1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76}, 58]]

Formula

G.f.: Sum_{k=0..6} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

A357072 Number of partitions of n into at most 4 distinct positive triangular numbers.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 0, 2, 3, 1, 1, 3, 2, 1, 4, 3, 0, 3, 2, 2, 4, 3, 3, 3, 1, 3, 3, 2, 4, 5, 4, 1, 5, 3, 2, 6, 3, 3, 6, 4, 2, 5, 4, 4, 5, 4, 2, 7, 5, 5, 7, 3, 4, 7, 4, 4, 8, 5, 4, 7, 6, 2, 7, 6, 5, 10, 5, 6, 7, 5, 7, 7, 6, 4, 10, 8, 3, 12, 6, 4, 11, 6, 5, 9, 7
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 25 2022

Keywords

Crossrefs

Cf. A000217, A024940, A341021, A347586, A347627, A347732, A357070, A357071.

A358009 Number of partitions of n into at most 4 distinct prime parts.

Original entry on oeis.org

1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 6, 5, 5, 7, 5, 9, 7, 9, 7, 9, 9, 11, 9, 12, 8, 13, 11, 14, 13, 13, 12, 16, 14, 18, 17, 16, 17, 20, 17, 23, 19, 21, 19, 24, 23, 28, 24, 26, 25, 26, 30, 30, 29, 29, 29, 32, 36, 37, 36, 32, 38, 35, 43, 41, 43, 20
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 24 2022

Keywords

Crossrefs

Cf. A000040, A000586, A219180, A219198, A223893, A347550, A347578, A347586, A347741, A358010, A358011.

A358025 Number of partitions of n into at most 4 distinct squarefree parts.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 3, 3, 4, 4, 5, 6, 6, 8, 9, 10, 13, 13, 15, 17, 20, 22, 24, 27, 31, 32, 34, 37, 41, 46, 47, 53, 59, 61, 64, 71, 77, 83, 84, 95, 102, 108, 110, 122, 131, 137, 139, 154, 165, 173, 175, 191, 205, 215, 215, 233, 250, 260, 261, 282, 299, 313, 310, 332, 353, 368
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 25 2022

Keywords

Crossrefs

Cf. A005117, A087188, A341073, A347586, A347655, A347779, A358023, A358024.

A358637 Number of partitions of n into at most 4 distinct prime powers (including 1).

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 13, 13, 17, 18, 19, 21, 24, 25, 27, 29, 32, 35, 35, 38, 42, 45, 46, 50, 54, 57, 57, 63, 65, 72, 70, 78, 79, 87, 82, 93, 93, 101, 97, 107, 107, 116, 112, 123, 122, 133, 127, 139, 137, 149, 140, 156, 154, 166, 158, 171, 168, 180, 174, 186
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 24 2022

Keywords

Crossrefs

Cf. A000961, A106244, A341141, A347586, A347645, A347764, A358635, A358636.

A358640 Number of partitions of n into at most 4 distinct nonprime parts.

Original entry on oeis.org

1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 3, 2, 2, 3, 4, 5, 5, 4, 6, 8, 8, 9, 11, 11, 13, 16, 17, 19, 21, 22, 26, 30, 30, 34, 39, 43, 47, 50, 53, 61, 67, 69, 76, 84, 89, 97, 106, 110, 121, 131, 139, 148, 160, 166, 181, 194, 204, 215, 233, 242, 262, 274, 289, 305, 329, 338, 361, 378
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 24 2022

Keywords

Crossrefs

Cf. A018252, A096258, A341462, A347586, A347662, A347797, A358638, A358639.

A357069 Number of partitions of n into at most 4 distinct positive squares.

Original entry on oeis.org

1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 1, 1, 2, 2, 0, 1, 1, 1, 1, 0, 2, 3, 1, 1, 4, 2, 0, 1, 2, 2, 1, 0, 1, 4, 2, 0, 2, 4, 1, 1, 3, 1, 1, 2, 3, 3, 1, 0, 3, 5, 2, 0, 2, 4, 2, 0, 1, 3, 2, 2, 4
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 25 2022

Keywords

Links

Crossrefs

Cf. A000290, A002635, A025435, A025443, A033461, A341040, A347534, A347586, A347711.

Formula

a(n) = Sum_{k=0..4} A341040(n,k). - Alois P. Heinz, Oct 25 2022
Showing 1-8 of 8 results.

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