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.

A325771 Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 2), for k = 0, 1.

Original entry on oeis.org

0, 1, 1, 2, 1, 5, 4, 8, 5, 15, 11, 24, 15, 39, 28, 58, 38, 90, 62, 130, 85, 190, 131, 268, 177, 379, 258, 522, 346, 722, 489, 974, 648, 1317, 890, 1754, 1168, 2330, 1572, 3058, 2042, 4010, 2699, 5200, 3475, 6731, 4532, 8642, 5783, 11068, 7446, 14076, 9430
Offset: 1

Views

Author

Clark Kimberling, Jun 05 2019

Keywords

Comments

Row n partitions A006128 into 2 parts, r(n,0) + r(n,1) = p(n) = A006128(n). What is the limiting behavior of r(n,0)/p(n)?

Examples

			First 15 rows:
    0    1
    1    2
    1    5
    4    8
    5   15
   11   24
   15   39
   28   58
   38   90
   62  130
   85  190
  131  268
  177  379
  258  522
  346  722

Links

Crossrefs

Cf. A006128, A066898, A066897, A325772, A325773, A325774.

Programs

  • Mathematica
    f[n_] := Mod[Flatten[IntegerPartitions[n]], 2];
Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1}]  (* A325771 array *)
Flatten[%] (* A325771 sequence *)

Formula

(row n) = (A066898(n), A066897(n)).

A325772 Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 3), for k = 0, 1, 2.

Original entry on oeis.org

0, 1, 0, 0, 2, 1, 1, 4, 1, 1, 8, 3, 2, 13, 5, 5, 21, 9, 7, 34, 13, 11, 52, 23, 19, 77, 32, 27, 114, 51, 40, 163, 72, 61, 232, 106, 85, 325, 146, 120, 450, 210, 170, 614, 284, 232, 836, 395, 316, 1120, 529, 433, 1494, 717, 576, 1976, 946, 767, 2599, 1264
Offset: 1

Views

Author

Clark Kimberling, Jun 05 2019

Keywords

Comments

Row n partitions A006128 into 3 parts, r(n,0) + r(n,1) + r(n,2) = p(n) = A006128(n). What is the limiting behavior of r(n,0)/p(n)?

Examples

			First 15 rows:
    0     1     0
    0     2     1
    1     4     1
    1     8     3
    2    13     5
    5    21     9
    7    34    13
   11    52    23
   19    77    32
   27   114    51
   40   163    72
   61   232   106
   85   325   146
  120   450   210
  170   614   264

Links

Crossrefs

Cf. A006128, A325771, A325773, A325774.

Programs

  • Mathematica
    f[n_] := Mod[Flatten[IntegerPartitions[n]], 3];
Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1,2}]  (* A325772 array *)
Flatten[%] (* A325772 sequence *)

A325773 Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 4), for k = 0, 1, 2, 3.

Original entry on oeis.org

0, 1, 0, 0, 0, 2, 1, 0, 0, 4, 1, 1, 1, 7, 3, 1, 1, 13, 4, 2, 2, 20, 9, 4, 3, 32, 12, 7, 7, 48, 21, 10, 9, 73, 29, 17, 15, 106, 47, 24, 21, 153, 64, 37, 34, 215, 97, 53, 46, 303, 131, 76, 68, 416, 190, 106, 92, 571, 254, 151, 134, 770, 355, 204, 178, 1037
Offset: 1

Views

Author

Clark Kimberling, Jun 05 2019

Keywords

Comments

Row n partitions A006128 into 4 parts, r(n,0) + r(n,1) + r(n,3) + r(n,4) = p(n) = A006128(n). What is the limiting behavior of r(n,0)/p(n)?

Examples

			First 15 rows:
   0      1      0      0
   0      2      1      0
   0      4      1      1
   1      7      3      1
   1     13      4      2
   2     20      9      4
   3     32     12      7
   7     48     21     10
   9     73     29     17
  15    106     47     24
  21    153     64     37
  34    215     97     53
  46    303    131     76
  68    416    190    106
  92    571    254    151

Links

Crossrefs

Cf. A006128, A325771, A325772, A325774.

Programs

  • Mathematica
    f[n_] := Mod[Flatten[IntegerPartitions[n]], 4];
Table[Count[f[n], k], {n, 1, 40}, {k,0,1,2,3}]  (* A325773 array *)
Flatten[%] (* A325773 sequence *)
Showing 1-3 of 3 results.

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

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