This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A194447 Rank of the n-th region of the set of partitions of j, if 1<=n<=A000041(j). 33
 0, 0, 0, 1, -1, 2, -2, 1, 2, 2, -5, 2, 3, 3, -8, 1, 2, 2, 2, 4, 3, -14, 2, 3, 3, 3, 2, 4, 4, -21, 1, 2, 2, 2, 4, 3, 1, 3, 5, 5, 4, -32, 2, 3, 3, 3, 2, 4, 4, 1, 4, 3, 5, 6, 5, -45, 1, 2, 2, 2, 4, 3, 1, 3, 5, 5, 4, -2, 2, 4, 4, 5, 3, 6, 6, 5, -65 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Here the rank of a "region" is defined to be the largest part minus the number of parts (the same idea as the Dyson's rank of a partition). Also triangle read by rows: T(j,k) = rank of the k-th region of the last section of the set of partitions of j. The sum of every row is equal to zero. Note that in some rows there are several negative terms. - Omar E. Pol, Oct 27 2012 For the definition of "region" see A206437. See also A225600 and A225610. - Omar E. Pol, Aug 12 2013 LINKS FORMULA a(n) = A141285(n) - A194446(n). - Omar E. Pol, Dec 05 2011 EXAMPLE In the triangle T(j,k) for j = 6 the number of regions in the last section of the set of partitions of 6 is equal to 4. The first region given by [2] has rank 2-1 = 1. The second region given by [4,2] has rank 4-2 = 2. The third region given by [3] has rank 3-1 = 2. The fourth region given by [6,3,2,2,1,1,1,1,1,1,1] has rank 6-11 = -5 (see below): From Omar E. Pol, Aug 12 2013: (Start) --------------------------------------------------------- .    Regions       Illustration of ranks of the regions --------------------------------------------------------- .    For J=6        k=1     k=2      k=3        k=4 .  _ _ _ _ _ _                              _ _ _ _ _ _ . |_ _ _      |                     _ _ _   .          | . |_ _ _|_    |           _ _ _ _   * * .|    .        | . |_ _    |   |     _ _   * * .  |              .      | . |_ _|_ _|_  |     * .|        .|                .    | .           | |                                     .  | .           | |                                       .| .           | |                                       *| .           | |                                       *| .           | |                                       *| .           | |                                       *| .           |_|                                       *| . So row 6 lists:     1       2         2              -5 (End) Written as a triangle begins: 0; 0; 0; 1,-1; 2,-2; 1,2,2,-5; 2,3,3,-8; 1,2,2,2,4,3,-14; 2,3,3,3,2,4,4,-21; 1,2,2,2,4,3,1,3,5,5,4,-32; 2,3,3,3,2,4,4,1,4,3,5,6,5,-45; 1,2,2,2,4,3,1,3,5,5,4,-2,2,4,4,5,3,6,6,5,-65; 2,3,3,3,2,4,4,1,4,3,5,6,5,-3,3,5,5,4,5,4,7,7,6,-88; CROSSREFS Row j has length A187219(j). The absolute value of the last term of row j is A000094(j+1). Row sums give A000004. Cf. A000041, A002865, A135010, A138121, A138137, A138879, A186114, A186412, A193870, A194436, A194437, A194438, A194439, A194446, A206437. Sequence in context: A156748 A075445 A216612 * A236573 A293375 A232174 Adjacent sequences:  A194444 A194445 A194446 * A194448 A194449 A194450 KEYWORD sign,tabf AUTHOR Omar E. Pol, Dec 04 2011 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.

Last modified February 18 02:15 EST 2019. Contains 320237 sequences. (Running on oeis4.)