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 1-3 of 3 results.

A347586 Number of partitions of n into at most 4 distinct parts.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 26, 31, 36, 43, 49, 57, 65, 75, 84, 96, 107, 121, 134, 150, 165, 184, 201, 222, 242, 266, 288, 315, 340, 370, 398, 431, 462, 499, 533, 573, 611, 655, 696, 744, 789, 841, 890, 946, 999, 1060, 1117, 1182, 1244, 1314, 1380, 1455
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 08 2021

Keywords

Links

Crossrefs

Cf. A000578, A001400, A014591, A065033, A347587, A347588.

Programs

  • Mathematica
    nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 4}], {x, 0, nmax}], x]
Join[{1}, LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10}, 60]]

Formula

G.f.: Sum_{k=0..4} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).
a(n) ~ A000578(n)/144. - Stefano Spezia, Sep 08 2021

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).

A358010 Number of partitions of n into at most 5 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, 6, 7, 6, 9, 7, 9, 9, 9, 11, 11, 11, 13, 12, 13, 15, 15, 17, 15, 18, 17, 20, 20, 23, 20, 25, 22, 27, 28, 28, 27, 30, 29, 36, 34, 38, 36, 41, 35, 48, 41, 48, 44, 50, 46, 58, 53, 61, 54, 64, 55, 72, 66, 74
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 24 2022

Keywords

Crossrefs

Cf. A000040, A000586, A219180, A219199, A223893, A347550, A347587, A347609, A347742, A358009, A358011.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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