A309626 Sum of the even parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 12, 18, 38, 60, 104, 136, 218, 294, 432, 568, 802, 1036, 1424, 1794, 2382, 2986, 3866, 4754, 6054, 7370, 9208, 11092, 13666, 16322, 19864, 23504, 28272, 33244, 39592, 46170, 54522, 63212, 74040, 85316, 99208, 113716, 131392

Offset

0,9

Links

Harvey P. Dale, Table of n, a(n) for n = 0..100

Index entries for sequences related to partitions

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/2)} o * ((o-1) mod 2) + m * ((m-1) mod 2) + l * ((l-1) mod 2) + k * ((k-1) mod 2) + j * ((j-1) mod 2) + i * ((i-1) mod 2) + (n-i-j-k-l-m-o) * ((n-i-j-k-l-m-o-1) mod 2).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[i * Mod[i - 1, 2] + j * Mod[j - 1, 2] + k * Mod[k - 1, 2] + l * Mod[l - 1, 2] + m * Mod[m - 1, 2] + o * Mod[o - 1, 2] + (n - i - j - k - l - m - o) * Mod[n - i - j - k - l - m - o - 1, 2], {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]
Table[Total[Select[Flatten[IntegerPartitions[n, {7}]], EvenQ]], {n, 0, 50}] (* Harvey P. Dale, Oct 02 2019 *)

Crossrefs

Sequence in context: A052289 A309547 A309552 * A309632 A309659 A309664

Adjacent sequences: A309623 A309624 A309625 * A309627 A309628 A309629

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 10 2019

Status

approved