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A309551
Number of even parts in the partitions of n into 6 parts.
0
0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 8, 15, 24, 32, 44, 62, 82, 108, 140, 179, 226, 284, 348, 427, 520, 623, 744, 887, 1046, 1228, 1434, 1668, 1930, 2225, 2550, 2917, 3326, 3772, 4266, 4817, 5416, 6076, 6798, 7586, 8446, 9383, 10394, 11498, 12694, 13979, 15368
OFFSET
0,9
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-1) mod 2) + ((j-1) mod 2) + ((k-1) mod 2) + ((l-1) mod 2) + ((m-1) mod 2) + ((n-i-j-k-l-m-1) mod 2)).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[ Mod[i - 1, 2] + Mod[j - 1, 2] + Mod[k - 1, 2] + Mod[l - 1, 2] + Mod[m - 1, 2] + 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[Count[Flatten[IntegerPartitions[n, {6}]], _?EvenQ], {n, 0, 50}] (* Harvey P. Dale, Oct 04 2019 *)
CROSSREFS
Sequence in context: A073335 A239258 A362864 * A309625 A309630 A309658
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 07 2019
STATUS
approved