A326589 Sum of the smallest parts of the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 43, 56, 77, 100, 133, 171, 223, 282, 362, 453, 573, 709, 884, 1084, 1337, 1626, 1984, 2394, 2896, 3468, 4163, 4951, 5897, 6972, 8249, 9696, 11402, 13330, 15586, 18131, 21091, 24417, 28264, 32580

Offset

0,13

Links

Table of n, a(n) for n=0..53.

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.

a(n) = A326588(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[r, {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}]

Crossrefs

Cf. A026816, A326588, A326590, A326591, A326592, A326593, A326594, A326595, A326596, A326597, A326598.

Sequence in context: A084251 A218026 A241728 * A024794 A326292 A195308

Adjacent sequences: A326586 A326587 A326588 * A326590 A326591 A326592

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved