A308867 Sum of all the parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 6, 7, 16, 27, 50, 77, 132, 182, 280, 390, 560, 748, 1044, 1349, 1800, 2310, 2992, 3749, 4776, 5875, 7332, 8937, 10948, 13166, 15960, 18972, 22688, 26763, 31654, 36995, 43416, 50320, 58520, 67431, 77800, 89052, 102144, 116186, 132396, 149895

Offset

0,7

Links

Table of n, a(n) for n=0..45.

Index entries for sequences related to partitions

Formula

a(n) = 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)} 1.

a(n) = n * A238340(n).

a(n) = A308868(n) + A308869(n) + A306670(n) + A306671(n) + A308872(n) + A308873(n).

Mathematica

Table[n*Sum[Sum[Sum[Sum[Sum[1, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 100}]
Table[Total[Flatten[IntegerPartitions[n, {6}]]], {n, 0, 50}] (* Harvey P. Dale, Oct 29 2024 *)

Crossrefs

Cf. A238340, A308868, A308869, A306670, A306671, A308872, A308873.

Sequence in context: A315845 A322638 A309481 * A315846 A062850 A139450

Adjacent sequences: A308864 A308865 A308866 * A308868 A308869 A308870

Keyword

nonn,changed

Author

Wesley Ivan Hurt, Jun 29 2019

Status

approved