A039837 Number of partitions satisfying cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5).

1, 1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 79, 105, 136, 176, 223, 288, 361, 462, 575, 725, 899, 1123, 1388, 1715, 2108, 2592, 3160, 3872, 4694, 5712, 6905, 8348, 10059, 12101, 14514, 17397, 20774, 24822, 29518, 35131, 41664, 49378, 58416, 68982, 81341, 95810, 112595, 132299, 155027, 181623, 212345, 248042

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 and 0 <= 4 (AA).

Links

Table of n, a(n) for n=0..54.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] <= c[1] && c[0] <= c[4]];
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: A035993 A036004 A027339 * A039838 A064173 A145724

Adjacent sequences: A039834 A039835 A039836 * A039838 A039839 A039840

Keyword

nonn,changed

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Jean-François Alcover, Oct 11 2024

Status

approved