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 1-7 of 7 results.

A347548 Number of partitions of n into 3 or more distinct parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 9, 11, 15, 19, 24, 29, 37, 44, 54, 65, 78, 92, 110, 129, 152, 178, 208, 241, 281, 324, 374, 431, 495, 567, 650, 741, 845, 962, 1093, 1239, 1405, 1588, 1794, 2025, 2281, 2566, 2886, 3239, 3633, 4071, 4556, 5093, 5691, 6350, 7080, 7888, 8779, 9762, 10850
Offset: 6

Views

Author

Ilya Gutkovskiy, Sep 06 2021

Keywords

Crossrefs

Cf. A000009, A004526, A111133, A347549.

Programs

  • Mathematica
    nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 3, nmax}], {x, 0, nmax}], x] // Drop[#, 6] &

Formula

G.f.: Sum_{k>=3} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).
a(n) = A000009(n) - floor((n + 1)/2). - Vaclav Kotesovec, Sep 14 2021

A347574 Number of partitions of n into 7 or more distinct parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 52, 70, 89, 116, 146, 186, 231, 289, 354, 437, 530, 645, 775, 934, 1112, 1327, 1569, 1856, 2179, 2559, 2985, 3483, 4040, 4684, 5406, 6235, 7160, 8218, 9396, 10735, 12225, 13910, 15780, 17888, 20223, 22842, 25742, 28983, 32562
Offset: 28

Views

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

Links

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347575, A347576, A347577.

Programs

  • Mathematica
    nmax = 77; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 7, nmax}], {x, 0, nmax}], x] // Drop[#, 28] &

Formula

G.f.: Sum_{k>=7} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

A347572 Number of partitions of n into 5 or more distinct parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 72, 91, 112, 139, 168, 206, 246, 297, 353, 420, 494, 584, 682, 798, 927, 1077, 1243, 1437, 1649, 1894, 2166, 2475, 2817, 3207, 3636, 4121, 4658, 5261, 5926, 6673, 7494, 8412, 9425, 10550, 11788, 13166, 14677, 16352
Offset: 15

Views

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

Crossrefs

Cf. A111133, A347548, A347549, A347573, A347574, A347575, A347576, A347577.

Programs

  • Mathematica
    nmax = 65; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 5, nmax}], {x, 0, nmax}], x] // Drop[#, 15] &

Formula

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

A347573 Number of partitions of n into 6 or more distinct parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 38, 49, 65, 82, 105, 132, 165, 203, 251, 305, 371, 447, 537, 640, 763, 901, 1063, 1248, 1461, 1702, 1981, 2294, 2652, 3056, 3514, 4028, 4611, 5261, 5994, 6814, 7732, 8754, 9900, 11170, 12587, 14160, 15906, 17839, 19985, 22352
Offset: 21

Views

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347574, A347575, A347576, A347577.

Programs

  • Mathematica
    nmax = 70; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 6, nmax}], {x, 0, nmax}], x] // Drop[#, 21] &

Formula

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

A347575 Number of partitions of n into 8 or more distinct parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 73, 94, 123, 157, 201, 252, 318, 394, 489, 600, 735, 892, 1083, 1302, 1564, 1867, 2224, 2634, 3116, 3665, 4305, 5035, 5877, 6834, 7935, 9179, 10601, 12208, 14033, 16087, 18415, 21024, 23968, 27264, 30965, 35097, 39728, 44881
Offset: 36

Views

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347574, A347576, A347577.

Programs

  • Mathematica
    nmax = 85; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 8, nmax}], {x, 0, nmax}], x] // Drop[#, 36] &

Formula

G.f.: Sum_{k>=8} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

A347576 Number of partitions of n into 9 or more distinct parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 97, 128, 164, 212, 267, 340, 423, 530, 654, 808, 986, 1207, 1460, 1768, 2123, 2549, 3037, 3620, 4284, 5069, 5965, 7012, 8203, 9590, 11160, 12975, 15029, 17388, 20048, 23092, 26513, 30408, 34781, 39734, 45278
Offset: 45

Views

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347574, A347575, A347577.

Programs

  • Mathematica
    nmax = 92; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 9, nmax}], {x, 0, nmax}], x] // Drop[#, 45] &

Formula

G.f.: Sum_{k>=9} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

A347577 Number of partitions of n into 10 or more distinct parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 131, 169, 219, 278, 355, 445, 560, 695, 863, 1061, 1304, 1588, 1933, 2336, 2819, 3381, 4050, 4824, 5738, 6793, 8028, 9450, 11105, 13000, 15195, 17702, 20588, 23874, 27640, 31913, 36790, 42308, 48578, 55654, 63666
Offset: 55

Views

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347574, A347575, A347576.

Programs

  • Mathematica
    nmax = 103; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 10, nmax}], {x, 0, nmax}], x] // Drop[#, 55] &

Formula

G.f.: Sum_{k>=10} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).
Showing 1-7 of 7 results.

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