A309552 Sum of the even parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 0, 2, 4, 12, 18, 38, 60, 90, 124, 192, 260, 368, 488, 666, 864, 1148, 1442, 1862, 2328, 2918, 3574, 4442, 5376, 6552, 7838, 9444, 11192, 13328, 15628, 18432, 21492, 25076, 28972, 33610, 38588, 44402, 50680, 57942, 65780, 74772, 84392, 95428

Offset

0,8

Links

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

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[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] + (n - i - j - k - l - m) * Mod[n - i - j - k - l - m - 1, 2], {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
Table[Total[Select[Flatten[IntegerPartitions[n, {6}]], EvenQ]], {n, 0, 50}] (* Harvey P. Dale, Jun 23 2022 *)

Crossrefs

Sequence in context: A198392 A052289 A309547 * A309626 A309632 A309659

Adjacent sequences: A309549 A309550 A309551 * A309553 A309554 A309555

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 07 2019

Status

approved