A039842 Number of partitions satisfying cn(0,5) < cn(1,5) + cn(4,5).

1, 1, 2, 4, 5, 8, 12, 17, 24, 34, 45, 63, 84, 111, 148, 193, 251, 326, 417, 536, 678, 862, 1083, 1360, 1701, 2116, 2624, 3248, 3996, 4915, 6015, 7349, 8948, 10875, 13171, 15932, 19207, 23121, 27760, 33274, 39789, 47504, 56592, 67320, 79909, 94738, 112079, 132436, 156212, 183998, 216399, 254166, 298066, 349148

Offset

1,3

Comments

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

Short: 0 < 1 + 4 (ZMAAp).

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[1] + c[4]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 54}] (* Jean-François Alcover, Oct 11 2024 *)

Crossrefs

Sequence in context: A335702 A069259 A102186 * A188216 A238395 A116901

Adjacent sequences: A039839 A039840 A039841 * A039843 A039844 A039845

Keyword

nonn,changed

Author

Olivier Gérard

Status

approved