A308827 Sum of the largest parts of the partitions of n into 5 parts.

0, 0, 0, 0, 0, 1, 2, 5, 9, 17, 27, 44, 64, 96, 134, 188, 251, 339, 439, 571, 724, 917, 1137, 1411, 1719, 2097, 2519, 3023, 3586, 4253, 4990, 5848, 6797, 7891, 9092, 10467, 11966, 13670, 15526, 17612, 19880, 22417, 25159, 28209, 31502, 35145, 39061, 43375

Offset

0,7

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (n-i-j-k-l).

a(n) = A308822(n) - A308823(n) - A308824(n) - A308825(n) - A308826(n).

Example

The partitions of n into 5 parts for n = 10, 11, ..
                                                       1+1+1+1+10
                                                        1+1+1+2+9
                                                        1+1+1+3+8
                                                        1+1+1+4+7
                                                        1+1+1+5+6
                                            1+1+1+1+9   1+1+2+2+8
                                            1+1+1+2+8   1+1+2+3+7
                                            1+1+1+3+7   1+1+2+4+6
                                            1+1+1+4+6   1+1+2+5+5
                                            1+1+1+5+5   1+1+3+3+6
                                1+1+1+1+8   1+1+2+2+7   1+1+3+4+5
                                1+1+1+2+7   1+1+2+3+6   1+1+4+4+4
                                1+1+1+3+6   1+1+2+4+5   1+2+2+2+7
                    1+1+1+1+7   1+1+1+4+5   1+1+3+3+5   1+2+2+3+6
                    1+1+1+2+6   1+1+2+2+6   1+1+3+4+4   1+2+2+4+5
                    1+1+1+3+5   1+1+2+3+5   1+2+2+2+6   1+2+3+3+5
        1+1+1+1+6   1+1+1+4+4   1+1+2+4+4   1+2+2+3+5   1+2+3+4+4
        1+1+1+2+5   1+1+2+2+5   1+1+3+3+4   1+2+2+4+4   1+3+3+3+4
        1+1+1+3+4   1+1+2+3+4   1+2+2+2+5   1+2+3+3+4   2+2+2+2+6
        1+1+2+2+4   1+1+3+3+3   1+2+2+3+4   1+3+3+3+3   2+2+2+3+5
        1+1+2+3+3   1+2+2+2+4   1+2+3+3+3   2+2+2+2+5   2+2+2+4+4
        1+2+2+2+3   1+2+2+3+3   2+2+2+2+4   2+2+2+3+4   2+2+3+3+4
        2+2+2+2+2   2+2+2+2+3   2+2+2+3+3   2+2+3+3+3   2+3+3+3+3
--------------------------------------------------------------------------
  n  |     10          11          12          13          14        ...
--------------------------------------------------------------------------
a(n) |     27          44          64          96         134        ...
--------------------------------------------------------------------------
- Wesley Ivan Hurt, Sep 12 2019

Mathematica

Table[Sum[Sum[Sum[Sum[n - i - j - k - l, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 100}]

Crossrefs

Cf. A026811, A308822, A308823, A308824, A308825, A308826.

Sequence in context: A062492 A268346 A165271 * A139672 A308873 A308933

Adjacent sequences: A308824 A308825 A308826 * A308828 A308829 A308830

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 26 2019

Status

approved