A039841 Number of partitions satisfying cn(0,5) < cn(2,5) + cn(3,5).

0, 1, 2, 3, 4, 7, 10, 15, 21, 30, 41, 56, 74, 101, 134, 177, 228, 297, 382, 493, 626, 794, 999, 1260, 1575, 1967, 2439, 3022, 3724, 4587, 5618, 6874, 8374, 10189, 12351, 14953, 18041, 21740, 26116, 31329, 37483, 44793, 53392, 63555, 75482, 75482, 89537, 105998, 125326, 147885, 174295, 205071, 241000, 282758

Offset

1,3

Comments

For a given partition cn(i,n) means the number of its parts equal to i modulo n.

Short: 0 < 2 + 3 (ZMBBp).

Links

Table of n, a(n) for n=1..54.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] < c[2] + c[3]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 53}] (* Jean-François Alcover, Oct 11 2024 *)

Crossrefs

Sequence in context: A330357 A145467 A325341 * A078159 A129490 A018132

Adjacent sequences: A039838 A039839 A039840 * A039842 A039843 A039844

Keyword

nonn

Author

Olivier Gérard

Status

approved