A309629 Sum of the odd parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 8, 7, 16, 21, 42, 53, 94, 121, 200, 261, 396, 516, 758, 973, 1358, 1732, 2352, 2956, 3898, 4860, 6286, 7759, 9840, 12038, 15064, 18254, 22510, 27071, 33014, 39386, 47522, 56293, 67320, 79222, 93910, 109848, 129294, 150344, 175706

Offset

0,9

Links

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

Index entries for sequences related to partitions

Formula

a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} i * (i mod 2) + j * (j mod 2) + k * (k mod 2) + l * (l mod 2) + m * (m mod 2) + o * (o mod 2) + p * (p mod 2) + (n-i-j-k-l-m-o-p) * ((n-i-j-k-l-m-o-p) mod 2).

Mathematica

Table[Total[Select[Flatten[IntegerPartitions[n, {8}]], OddQ]], {n, 0, 50}] (* Harvey P. Dale, Nov 20 2022 *)

Crossrefs

Sequence in context: A298666 A309628 A303716 * A075573 A317706 A302677

Adjacent sequences: A309626 A309627 A309628 * A309630 A309631 A309632

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 10 2019

Status

approved