A326685 Sum of the fourth largest parts of the partitions of n into 10 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 5, 7, 10, 10, 14, 18, 22, 23, 33, 32, 44, 49, 60, 65, 88, 83, 116, 120, 145, 148, 196, 189, 250, 242, 301, 299, 395, 359, 478, 454, 570, 543, 718, 649, 864, 788, 1016, 952, 1255, 1102

Offset

0,21

Links

Table of n, a(n) for n=0..63.

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)} c(r) * c(q) * c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p-q-r) * k, where c = A010051.

a(n) = A326678(n) - A326679(n) - A326680(n) - A326681(n) - A326682(n) - A326683(n) - A326684(n) - A326686(n) - A326687(n) - A326688(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k * (PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[l] - PrimePi[l - 1]) (PrimePi[m] - PrimePi[m - 1]) (PrimePi[o] - PrimePi[o - 1]) (PrimePi[p] - PrimePi[p - 1]) (PrimePi[q] - PrimePi[q - 1]) (PrimePi[r] - PrimePi[r - 1]) (PrimePi[n - i - j - k - l - m - o - p - q - r] - PrimePi[n - i - j - k - l - m - o - p - q - r - 1]), {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. A010051, A259201, A326678, A326679, A326680, A326681, A326682, A326683, A326684, A326686, A326687, A326688.

Sequence in context: A308978 A326460 A326546 * A274150 A057591 A024405

Adjacent sequences: A326682 A326683 A326684 * A326686 A326687 A326688

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 17 2019

Status

approved