A326598 - OEIS

A326598

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

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 17, 27, 46, 69, 108, 158, 234, 329, 471, 645, 891, 1198, 1614, 2125, 2808, 3637, 4718, 6029, 7699, 9709, 12243, 15265, 19013, 23473, 28933, 35381, 43211, 52396, 63436, 76343, 91710, 109580, 130720, 155171, 183884

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OFFSET

0,12

LINKS

Table of n, a(n) for n=0..48.

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)} (n-i-j-k-l-m-o-p-q-r).

a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(n - i - j - k - l - m - o - p - q - 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, A326589, A326590, A326591, A326592, A326593, A326594, A326595, A326596, A326597.

Sequence in context: A308933 A308998 A326473 * A093694 A366738 A068006

Adjacent sequences: A326595 A326596 A326597 * A326599 A326600 A326601

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 13 2019

STATUS

approved