A308978 Sum of the fourth largest parts of the partitions of n into 7 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 5, 7, 10, 10, 11, 15, 16, 20, 24, 26, 32, 43, 40, 51, 55, 64, 70, 93, 81, 111, 102, 132, 128, 172, 139, 202, 182, 243, 209, 296, 233, 352, 287, 402, 336, 495, 372, 577, 458, 661, 520, 800, 585, 938, 683

Offset

0,15

Links

Table of n, a(n) for n=0..62.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} c(i) * c(j) * c(k) * c(l) * c(m) * c(o) * c(n-i-j-k-l-m-o) * k, where c = A010051.

a(n) = A308974(n) - A308975(n) - A308976(n) - A308977(n) - A308979(n) - A307637(n) - A308980(n).

Mathematica

Table[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[n - i - j - k - l - m - o] - PrimePi[n - i - j - k - l - m - o - 1]), {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Crossrefs

Cf. A010051, A259197, A307637, A308974, A308975, A308976, A308977, A308979, A308980.

Sequence in context: A152432 A308856 A308922 * A326460 A326546 A326685

Adjacent sequences: A308975 A308976 A308977 * A308979 A308980 A308981

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 04 2019

Status

approved