A309713 Sum of the odd parts appearing among the third largest parts of the partitions of n into 4 parts.

0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 7, 10, 17, 20, 27, 30, 42, 50, 67, 80, 102, 115, 144, 164, 200, 227, 270, 304, 363, 406, 474, 526, 603, 664, 761, 842, 959, 1051, 1179, 1282, 1434, 1561, 1737, 1888, 2088, 2252, 2480, 2672, 2928, 3148, 3432, 3680, 4009, 4289

Offset

0,7

Links

Table of n, a(n) for n=0..53.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} j * (j mod 2).

Example

Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
                                                         1+1+1+9
                                                         1+1+2+8
                                                         1+1+3+7
                                                         1+1+4+6
                                             1+1+1+8     1+1+5+5
                                             1+1+2+7     1+2+2+7
                                 1+1+1+7     1+1+3+6     1+2+3+6
                                 1+1+2+6     1+1+4+5     1+2+4+5
                                 1+1+3+5     1+2+2+6     1+3+3+5
                     1+1+1+6     1+1+4+4     1+2+3+5     1+3+4+4
         1+1+1+5     1+1+2+5     1+2+2+5     1+2+4+4     2+2+2+6
         1+1+2+4     1+1+3+4     1+2+3+4     1+3+3+4     2+2+3+5
         1+1+3+3     1+2+2+4     1+3+3+3     2+2+2+5     2+2+4+4
         1+2+2+3     1+2+3+3     2+2+2+4     2+2+3+4     2+3+3+4
         2+2+2+2     2+2+2+3     2+2+3+3     2+3+3+3     3+3+3+3
--------------------------------------------------------------------------
  n  |      8           9          10          11          12        ...
--------------------------------------------------------------------------
a(n) |      3           3           7          10          17        ...
--------------------------------------------------------------------------
- Wesley Ivan Hurt, Sep 08 2019

Mathematica

Table[Sum[Sum[Sum[j * Mod[j, 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 50}]

Crossrefs

Sequence in context: A032060 A241385 A307736 * A153903 A331729 A095741

Adjacent sequences: A309710 A309711 A309712 * A309714 A309715 A309716

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 13 2019

Status

approved