A309664 Sum of the even parts in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 12, 18, 38, 60, 104, 152, 250, 360, 524, 726, 1032, 1396, 1928, 2546, 3418, 4466, 5862, 7526, 9742, 12352, 15710, 19692, 24742, 30682, 38110, 46792, 57504, 70046, 85258, 102964, 124366, 149128, 178694, 212828, 253286

Offset

0,12

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} r * ((r-1) mod 2) + q * ((q-1) mod 2) + p * ((p-1) mod 2) + o * ((o-1) mod 2) + m * ((m-1) mod 2) + l * ((l-1) mod 2) + k * ((k-1) mod 2) + j * ((j-1) mod 2) + i * ((i-1) mod 2) + (n-i-j-k-l-m-o-p-q-r-1) * ((n-i-j-k-l-m-o-p-q-r-1) mod 2).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * Mod[i - 1, 2] + j * Mod[j - 1, 2] + k * Mod[k - 1, 2] + l * Mod[l - 1, 2] + m * Mod[m - 1, 2] + o * Mod[o - 1, 2] + p * Mod[p - 1, 2] + q * Mod[q - 1, 2] + r * Mod[r - 1, 2] + (n - i - j - k - l - m - o - p - q - r) * Mod[n - i - j - k - l - m - o - p - q - r - 1, 2], {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]
Table[Total[Select[Flatten[IntegerPartitions[n, {10}]], EvenQ]], {n, 0, 50}] (* Harvey P. Dale, Nov 01 2020 *)

Crossrefs

Sequence in context: A309626 A309632 A309659 * A024872 A129021 A290440

Adjacent sequences: A309661 A309662 A309663 * A309665 A309666 A309667

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 11 2019

Status

approved