A309800 Sum of the even parts appearing among the largest parts of the partitions of n into 4 parts.

0, 0, 0, 0, 0, 2, 2, 6, 6, 14, 18, 32, 38, 62, 72, 104, 122, 170, 200, 264, 302, 388, 444, 554, 628, 768, 866, 1036, 1160, 1376, 1532, 1788, 1976, 2280, 2518, 2880, 3160, 3590, 3920, 4410, 4802, 5374, 5838, 6492, 7018, 7766, 8378, 9224, 9922, 10878, 11674

Offset

0,6

Links

Table of n, a(n) for n=0..50.

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)} (n-i-j-k) * ((n-i-j-k-1) 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) |      6          14          18          32          38        ...
--------------------------------------------------------------------------
- Wesley Ivan Hurt, Sep 07 2019

Mathematica

Table[Sum[Sum[Sum[(n - i - j - k)*Mod[n - i - j - k - 1, 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: A285610 A056453 A244486 * A306007 A287603 A034422

Adjacent sequences: A309797 A309798 A309799 * A309801 A309802 A309803

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 17 2019

Status

approved