login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187219 Number of partitions of n that do not contain parts less than the smallest part of the partitions of n-1. 54
1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 210, 253, 320, 383, 478, 574, 708, 847, 1039, 1238, 1507, 1794, 2167, 2573, 3094, 3660, 4378, 5170, 6153, 7245, 8591, 10087, 11914, 13959, 16424, 19196, 22519, 26252, 30701, 35717 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Essentially the same as A002865, but here a(1) = 1 not 0.

Also number of regions in the last section of the set of partitions of n.

Also number of partitions of n+k that are formed by k+1 sections, k >= 0 (Cf. A194799). - Omar E. Pol, Jan 30 2012

For the definition of region see A206437. - Omar E. Pol, Aug 13 2013

Partial sums give A000041, n >= 1. - Omar E. Pol, Sep 04 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Omar E. Pol, Illustration of the seven regions of 5

FORMULA

a(n) = A083751(n) + 1. - Omar E. Pol, Mar 04 2012

a(n) = A002865(n), if n >= 2. - Omar E. Pol, Aug 13 2013

EXAMPLE

From Omar E. Pol, Aug 13 2013: (Start)

Illustration of initial terms as number of regions:

.                                           _ _ _ _ _ _

.                                          |_ _ _      |

.                                          |_ _ _|_    |

.                                          |_ _    |   |

.                               _ _ _ _ _  |_ _|_ _|_  |

.                              |_ _ _    |           | |

.                     _ _ _ _  |_ _ _|_  |           | |

.                    |_ _    |         | |           | |

.             _ _ _  |_ _|_  |         | |           | |

.       _ _  |_ _  |       | |         | |           | |

.   _  |_  |     | |       | |         | |           | |

.  |_|   |_|     |_|       |_|         |_|           |_|

.

.   1     1       1         2           2             4

.

(End)

MATHEMATICA

Join[{1}, Drop[CoefficientList[Series[1 / Product[(1 - x^k)^1, {k, 2, 50}], {x, 0, 50}], x], 2]] (* Vincenzo Librandi, Feb 15 2018 *)

CROSSREFS

Cf. A000041, A002865, A083751, A135010, A186114, A193870, A206437, A225600, A225610.

Sequence in context: A036000 A002865 A085811 * A317785 A014810 A318771

Adjacent sequences:  A187216 A187217 A187218 * A187220 A187221 A187222

KEYWORD

nonn,less

AUTHOR

Omar E. Pol, Dec 09 2011

EXTENSIONS

Better definition from Omar E. Pol, Sep 04 2013

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 December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)