login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A260669 Number of unordered pairs of partitions of n with no common parts. 3
0, 1, 2, 6, 8, 24, 30, 74, 110, 219, 309, 651, 870, 1608, 2394, 4085, 5756, 9931, 13785, 22724, 32300, 50404, 70862, 111540, 153756, 232868, 326259, 484090, 667015, 986082, 1345566, 1951216, 2673588, 3805742, 5179213, 7348514, 9895254, 13845750, 18681896 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = A054440(n) / 2.

EXAMPLE

n = 6 has A000041(6) = 11 partitions: [6], [5,1], [4,2], [4,1,1], [3,3], [3,2,1], [3,1,1,1], [2,2,2], [2,2,1,1], [2,1,1,1,1], [1,1,1,1,1,1]; the following table shows the number of common parts of the pairs of these partitions, e.g. row i, col f: number of common parts of [2,2,1,1] and [3,2,1] = 2:

. -------------------+---+---+---+---+---+---+---+---+---+---+---+

.                    | a | b | c | d | e | f | g | h | i | j | k |

. ---+---------------+---+---+---+---+---+---+---+---+---+---+---+

.  a | [6]           | 1                                         |

.  b | [5,1]         | 0   2                                     |

.  c | [4,2]         | 0   0   2                                 |

.  d | [4,1,1]       | 0   1   1   3                             |

.  e | [3,3]         | 0   0   0   0   2                         |

.  f | [3,2,1]       | 0   1   1   1   1   3                     |

.  g | [3,1,1,1]     | 0   1   0   2   1   2   4                 |

.  h | [2,2,2]       | 0   0   1   0   0   1   0   3             |

.  i | [2,2,1,1]     | 0   1   1   2   0   2   2   2   4         |

.  j | [2,1,1,1,1]   | 0   1   1   2   0   2   3   1   3   5     |

.  k | [1,1,1,1,1,1] | 0   1   0   2   0   1   3   0   2   4   6 |

. ---+---------------+---+---+---+---+---+---+---+---+---+---+---+

The table contains 24 zeros, therefore a(6) = 24.

PROG

(Haskell)

a260669 = flip div 2 . a054440

CROSSREFS

Cf. A000041, A054440.

Sequence in context: A081957 A334901 A279732 * A122758 A122756 A193946

Adjacent sequences:  A260666 A260667 A260668 * A260670 A260671 A260672

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 15 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 13 11:56 EDT 2021. Contains 342936 sequences. (Running on oeis4.)