login
A036804
Number of partitions satisfying (cn(0,5) <= cn(2,5) = cn(3,5)).
0
1, 1, 1, 1, 2, 3, 4, 4, 5, 7, 12, 14, 16, 18, 25, 38, 46, 50, 59, 78, 112, 133, 149, 172, 224, 301, 359, 402, 468, 589, 769, 908, 1025, 1185, 1468, 1856, 2185, 2466, 2849, 3467, 4301, 5024, 5685, 6538, 7862, 9576, 11138, 12589, 14447, 17171, 20643, 23877, 26987
OFFSET
0,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (0<=2=3).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[2] && c[2] == c[3]];
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
Sequence in context: A036808 A103750 A036805 * A180046 A008329 A064558
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved