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A309622 Number of odd parts in the partitions of n into 7 parts. 0
0, 0, 0, 0, 0, 0, 0, 7, 6, 12, 16, 27, 34, 53, 66, 97, 122, 168, 208, 281, 342, 443, 536, 678, 812, 1008, 1196, 1462, 1722, 2072, 2420, 2885, 3344, 3937, 4538, 5297, 6064, 7022, 7994, 9190, 10412, 11886, 13400, 15215, 17074, 19274, 21544, 24204, 26946, 30137 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..49.

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

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Mod[i, 2] + Mod[j, 2] + Mod[k, 2] + Mod[l, 2] + Mod[m, 2] + Mod[o, 2] + Mod[n - i - j - k - l - m - o, 2], {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Table[Count[Flatten[IntegerPartitions[n, {7}]], _?OddQ], {n, 0, 50}] (* Harvey P. Dale, Feb 28 2020 *)

CROSSREFS

Sequence in context: A085964 A281313 A082121 * A215338 A176414 A297153

Adjacent sequences:  A309619 A309620 A309621 * A309623 A309624 A309625

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 10 2019

STATUS

approved

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Last modified May 25 23:50 EDT 2020. Contains 334612 sequences. (Running on oeis4.)