OFFSET
0,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (0 := 0 and 2<=1 and 3<=1 and 2<=4 and 3<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] == 0 && c[2] <= c[1] &&
c[3] <= c[1] && c[2] <= c[4] &&
c[3] <= c[4]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 45}] (* Jean-François Alcover, Oct 10 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved