A308924 Sum of the second largest parts in the partitions of n into 6 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 5, 6, 8, 14, 11, 16, 20, 28, 27, 38, 35, 52, 51, 66, 60, 94, 74, 121, 112, 154, 136, 194, 162, 253, 205, 289, 246, 382, 283, 457, 365, 533, 415, 652, 475, 778, 554, 857, 642, 1048, 690, 1195, 835, 1345, 944, 1564

Offset

0,13

Links

Table of n, a(n) for n=0..60.

Index entries for sequences related to partitions

Formula

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

a(n) = A308919(n) - A308920(n) - A308921(n) - A308922(n) - A308923(n) - A308925(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {6}], AllTrue[#, PrimeQ]&][[All, 2]]], {n, 0, 60}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 29 2021 *)

Crossrefs

Cf. A010051, A259196, A308919, A308920, A308921, A308922, A308923, A308925.

Sequence in context: A017819 A274148 A050044 * A307637 A326462 A326548

Adjacent sequences: A308921 A308922 A308923 * A308925 A308926 A308927

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 30 2019

Status

approved