OFFSET
0,6
LINKS
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} [n-i-k = i*k] * (n-i-k), where [ ] is the Iverson bracket.
EXAMPLE
a(13) = 6 since we have 13 = 1+6+6, whose largest part is 6. Partitions not counted: 1+1+11, 1+2+10, 1+3+9, 1+4+8, 1+5+7, 2+2+9, 2+3+8, 2+4+7, 2+5+6, 3+3+7, 3+4+6, 3+5+5, 4+4+5.
MATHEMATICA
Table[Sum[Sum[(n - i - k) KroneckerDelta[(n - i - k), (i*k)], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 0, 100}]
PROG
(PARI) first(n) = {my(res = vector(n)); for(i = 1, n \ 2, for(j = i, n\i, c = i + j + i*j; if(c <= n, res[c] += i*j))); concat(0, res)} \\ David A. Corneth, Jan 07 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 04 2022
STATUS
approved