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.

Previous Showing 11-15 of 15 results.

A320693 Number of partitions of n with up to six distinct kinds of 1.

Original entry on oeis.org

1, 6, 16, 27, 38, 55, 82, 119, 168, 233, 319, 432, 578, 766, 1008, 1315, 1702, 2191, 2804, 3566, 4512, 5683, 7126, 8897, 11061, 13700, 16913, 20807, 25510, 31183, 38009, 46198, 56002, 67713, 81671, 98276, 117989, 141349, 168984, 201609, 240058, 285310, 338480
Offset: 0

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Author

Alois P. Heinz, Oct 19 2018

Keywords

Links

Crossrefs

Column k=6 of A292622.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i=1,
      binomial(6, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);

Formula

a(n) ~ Pi * 2^(7/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^6 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021

A320694 Number of partitions of n with up to seven distinct kinds of 1.

Original entry on oeis.org

1, 7, 22, 43, 65, 93, 137, 201, 287, 401, 552, 751, 1010, 1344, 1774, 2323, 3017, 3893, 4995, 6370, 8078, 10195, 12809, 16023, 19958, 24761, 30613, 37720, 46317, 56693, 69192, 84207, 102200, 123715, 149384, 179947, 216265, 259338, 310333, 370593, 441667
Offset: 0

Views

Author

Alois P. Heinz, Oct 19 2018

Keywords

Links

Crossrefs

Column k=7 of A292622.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i=1,
      binomial(7, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);

Formula

a(n) ~ Pi * 2^(9/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^7 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021

A320695 Number of partitions of n with up to eight distinct kinds of 1.

Original entry on oeis.org

1, 8, 29, 65, 108, 158, 230, 338, 488, 688, 953, 1303, 1761, 2354, 3118, 4097, 5340, 6910, 8888, 11365, 14448, 18273, 23004, 28832, 35981, 44719, 55374, 68333, 84037, 103010, 125885, 153399, 186407, 225915, 273099, 329331, 396212, 475603, 569671, 680926
Offset: 0

Views

Author

Alois P. Heinz, Oct 19 2018

Keywords

Links

Crossrefs

Column k=8 of A292622.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i=1,
      binomial(8, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);

Formula

a(n) ~ Pi * 2^(11/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^8 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021

A320696 Number of partitions of n with up to nine distinct kinds of 1.

Original entry on oeis.org

1, 9, 37, 94, 173, 266, 388, 568, 826, 1176, 1641, 2256, 3064, 4115, 5472, 7215, 9437, 12250, 15798, 20253, 25813, 32721, 41277, 51836, 64813, 80700, 100093, 123707, 152370, 187047, 228895, 279284, 339806, 412322, 499014, 602430, 725543, 871815, 1045274
Offset: 0

Views

Author

Alois P. Heinz, Oct 19 2018

Keywords

Links

Crossrefs

Column k=9 of A292622.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i=1,
      binomial(9, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);

Formula

a(n) ~ Pi * 2^(13/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^9 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021

A320697 Number of partitions of n with up to ten distinct kinds of 1.

Original entry on oeis.org

1, 10, 46, 131, 267, 439, 654, 956, 1394, 2002, 2817, 3897, 5320, 7179, 9587, 12687, 16652, 21687, 28048, 36051, 46066, 58534, 73998, 93113, 116649, 145513, 180793, 223800, 276077, 339417, 415942, 508179, 619090, 752128, 911336, 1101444, 1327973, 1597358
Offset: 0

Views

Author

Alois P. Heinz, Oct 19 2018

Keywords

Links

Crossrefs

Column k=10 of A292622.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i=1,
      binomial(10, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);

Formula

a(n) ~ Pi * 2^(15/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^10 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021
Previous Showing 11-15 of 15 results.

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