A309551 Number of even parts in the partitions of n into 6 parts.

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

Links

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

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-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[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

Adjacent sequences: A309548 A309549 A309550 * A309552 A309553 A309554

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 07 2019

Status

approved