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 1-4 of 4 results.

A284616 Number of partitions of n such that the (sum of distinct even parts) < n/2.

Original entry on oeis.org

1, 1, 2, 2, 6, 8, 11, 14, 23, 29, 38, 48, 81, 102, 131, 163, 235, 293, 364, 448, 622, 762, 933, 1134, 1571, 1906, 2311, 2784, 3682, 4425, 5305, 6339, 8219, 9796, 11648, 13808, 17543, 20743, 24484, 28817, 36600, 43025, 50477, 59101, 73401, 85788, 100085
Offset: 1

Views

Author

Clark Kimberling, Apr 02 2017

Keywords

Examples

			a(4) counts these 2 partitions: 31, 1111.

Crossrefs

Cf. A284617, A284618, A284619.

Programs

  • Mathematica
    Table[p = IntegerPartitions[n];
Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,
     Length[p]}], # < n/2 &]], {n, 54}]

A284619 Number of partitions of n such that the (sum of distinct even parts) >= n/2.

Original entry on oeis.org

0, 1, 1, 3, 1, 3, 4, 8, 7, 13, 18, 29, 20, 33, 45, 68, 62, 92, 126, 179, 170, 240, 322, 441, 387, 530, 699, 934, 883, 1179, 1537, 2010, 1924, 2514, 3235, 4169, 4094, 5272, 6701, 8521, 7983, 10149, 12784, 16074, 15733, 19770, 24669, 30726, 29682, 36968, 45755
Offset: 1

Views

Author

Clark Kimberling, Apr 02 2017

Keywords

Comments

The number of partitions of n such that (sum distinct even parts) = n/2 is A284617(n)-A284616(n) = A284619(n)-A284618(n) = 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 15, 0, 0, 0, 23, 0, 0, 0, 55, 0, 0, 0, 153, 0, 0, 0, 265,... (offset 1, nonzero for 4|n) - R. J. Mathar, Aug 14 2023

Examples

			a(4) counts these 3 partitions: 4, 22, 211.

Crossrefs

Cf. A284616, A284617, A284618.

Programs

  • Mathematica
    Table[p = IntegerPartitions[n];
Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,
     Length[p]}], # >= n/2 &]], {n, 54}]

A284618 Number of partitions of n such that the (sum of distinct even parts) > n/2.

Original entry on oeis.org

0, 1, 1, 1, 1, 3, 4, 5, 7, 13, 18, 14, 20, 33, 45, 45, 62, 92, 126, 124, 170, 240, 322, 288, 387, 530, 699, 669, 883, 1179, 1537, 1475, 1924, 2514, 3235, 3181, 4094, 5272, 6701, 6279, 7983, 10149, 12784, 12494, 15733, 19770, 24669, 23785, 29682, 36968, 45755
Offset: 1

Views

Author

Clark Kimberling, Apr 02 2017

Keywords

Examples

			a(6) counts these 3 partitions: 6, 41, 411.

Crossrefs

Cf. A284616, A284617, A284619.

Programs

  • Mathematica
    Table[p = IntegerPartitions[n];
Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,
     Length[p]}], # > n/2 &]], {n, 54}]

A284610 Number of partitions of n such that the (sum of distinct even parts) = floor(n/2).

Original entry on oeis.org

1, 0, 0, 2, 3, 0, 0, 3, 4, 0, 0, 15, 20, 0, 0, 23, 31, 0, 0, 55, 70, 0, 0, 153, 195, 0, 0, 265, 335, 0, 0, 535, 664, 0, 0, 988, 1208, 0, 0, 2242, 2750, 0, 0, 3580, 4332, 0, 0, 6941, 8349, 0, 0, 11621, 13909, 0, 0, 20681, 24585, 0, 0, 37202
Offset: 1

Views

Author

Clark Kimberling, Mar 30 2017

Keywords

Examples

			a(5) counts these 3 partitions: 32, 221, 2111.

Crossrefs

Cf. A284608, A284616, A284617.

Programs

  • Mathematica
    Table[p = IntegerPartitions[n];
  Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k, Length[p]}], # == Floor[n/2] &]], {n, 60}](* Peter J. C. Moses, Mar 29 2017 *)
Showing 1-4 of 4 results.

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

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