login
A039843
Number of partitions satisfying cn(0,5) <= cn(1,5) + cn(2,5) and cn(0,5) <= cn(4,5) + cn(2,5) and cn(0,5) <= cn(1,5) + cn(3,5) and cn(0,5) <= cn(4,5) + cn(3,5).
0
1, 1, 2, 3, 5, 6, 10, 13, 19, 25, 36, 46, 64, 82, 110, 144, 188, 239, 311, 393, 506, 635, 805, 1004, 1263, 1567, 1951, 2408, 2976, 3648, 4485, 5471, 6682, 8113, 9854, 11907, 14398, 17325, 20842, 24984, 29930, 35743, 42662, 50758, 60354, 71564, 84817, 100267, 118431, 139579, 164340, 193181, 226840, 265866, 311345
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
Sequence in context: A039838 A064173 A145724 * A305937 A286097 A287483
KEYWORD
nonn
STATUS
approved