A309625 Number of even parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 8, 15, 24, 39, 50, 74, 98, 135, 174, 232, 292, 381, 470, 595, 728, 904, 1086, 1330, 1582, 1906, 2246, 2676, 3126, 3687, 4272, 4989, 5746, 6657, 7610, 8754, 9954, 11373, 12862, 14608, 16440, 18573, 20806, 23384, 26094, 29194

Offset

0,10

Links

Table of n, a(n) for n=0..50.

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-1) mod 2) + ((m-1) mod 2) + ((l-1) mod 2) + ((k-1) mod 2) + ((j-1) mod 2) + ((i-1) mod 2) + ((n-i-j-k-l-m-o-1) mod 2).

Mathematica

Table[Count[Flatten[IntegerPartitions[n, {7}]], _?EvenQ], {n, 0, 50}] (* Harvey P. Dale, Dec 18 2021 *)

Crossrefs

Sequence in context: A239258 A362864 A309551 * A309630 A309658 A309662

Adjacent sequences: A309622 A309623 A309624 * A309626 A309627 A309628

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 10 2019

Status

approved