OFFSET
0,3
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: 0 <= 1 + 2 and 0 <= 4 + 2 and 0 <= 1 + 3 and 0 <= 4 + 3 (AAxBB).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[1] + c[2] && c[0] <= c[4] + c[2] &&
c[0] <= c[1] + c[3] && c[0] <= c[4] + c[3]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 54}] (* Jean-François Alcover, Oct 11 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved