A309550 Sum of the odd parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 6, 5, 12, 15, 32, 39, 72, 92, 156, 198, 300, 380, 556, 683, 936, 1162, 1550, 1887, 2448, 2957, 3758, 4495, 5572, 6614, 8122, 9528, 11496, 13435, 16026, 18563, 21924, 25244, 29548, 33821, 39212, 44650, 51464, 58244, 66616, 75123, 85440

Offset

0,7

Links

Table of n, a(n) for n=0..46.

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 mod 2) + j * (j mod 2) + k * (k mod 2) + l * (l mod 2) + m * (m mod 2) + (n-i-j-k-l-m) * ((n-i-j-k-l-m) mod 2)).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[i * Mod[i, 2] + j * Mod[j, 2] + k * Mod[k, 2] + l * Mod[l, 2] + m * Mod[m, 2] + (n - i - j - k - l - m) * Mod[n - i - j - k - l - m, 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, 100}]

Crossrefs

Sequence in context: A046615 A103132 A046627 * A274931 A120114 A123168

Adjacent sequences: A309547 A309548 A309549 * A309551 A309552 A309553

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 07 2019

Status

approved