OFFSET
0,6
COMMENTS
Are 1, 2, 4, 6, 12 the only zeros?
EXAMPLE
The a(3) = 1 through a(11) = 11 partitions:
{2,1} . {3,2} . {4,3} {4,3,1} {5,4} {5,3,2} {6,5}
{4,1} {5,2} {5,2,1} {6,3} {5,4,1} {7,4}
{6,1} {7,2} {6,3,1} {8,3}
{4,2,1} {8,1} {7,2,1} {9,2}
{4,3,2,1} {10,1}
{5,4,2}
{6,3,2}
{6,4,1}
{7,3,1}
{8,2,1}
{5,3,2,1}
MAPLE
a:= proc(m) option remember; local b; b:=
proc(n, i, t) option remember; `if`(i*(i+1)/2<n,
0, `if`(n=0, signum(irem(m, t)),
b(n, i-1, t)+b(n-i, min(n-i, i-1), t+1)))
end: `if`(m=0, 1, b(m$2, 0))
end:
seq(a(n), n=0..55); # Alois P. Heinz, Mar 16 2023
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!IntegerQ[Mean[#]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 11 2023
EXTENSIONS
a(31)-a(55) from Alois P. Heinz, Mar 16 2023
STATUS
approved