A308772 Sum of the third largest parts of the partitions of n into 4 prime parts.

0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 5, 5, 5, 7, 6, 8, 10, 12, 13, 20, 11, 20, 20, 27, 18, 34, 21, 44, 28, 44, 31, 59, 30, 65, 46, 79, 41, 96, 49, 115, 58, 117, 64, 157, 64, 170, 73, 179, 80, 214, 80, 243, 98, 245, 114, 307, 106, 332, 124, 352, 124, 399, 124

Offset

0,9

Links

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

Index entries for sequences related to partitions

Formula

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

a(n) = A308809(n) - A308771(n) - A308773(n) - A308774(n).

Mathematica

Table[Sum[Sum[Sum[j (PrimePi[k] - PrimePi[k - 1])*(PrimePi[j] - PrimePi[j - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i - j - k] - PrimePi[n - i - j - k - 1]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

Crossrefs

Cf. A010051, A259194, A308771, A308773, A308774, A308809.

Sequence in context: A168256 A123081 A020917 * A332966 A035643 A324925

Adjacent sequences: A308769 A308770 A308771 * A308773 A308774 A308775

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2019

Status

approved