A326594 Sum of the fifth largest parts of the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 19, 29, 42, 62, 85, 121, 164, 226, 303, 407, 534, 706, 912, 1184, 1511, 1930, 2433, 3072, 3831, 4776, 5900, 7281, 8909, 10898, 13223, 16031, 19312, 23231, 27787, 33194, 39444, 46806, 55292, 65219, 76603

Offset

0,13

Links

Table of n, a(n) for n=0..51.

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)} l.

a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[l, {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, A326589, A326590, A326591, A326592, A326593, A326595, A326596, A326597, A326598.

Sequence in context: A308929 A308994 A326469 * A045842 A324741 A200462

Adjacent sequences: A326591 A326592 A326593 * A326595 A326596 A326597

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved