login
A036823
Number of partitions satisfying (cn(2,5) = cn(3,5) = 0 and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).
0
1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7, 8, 10, 11, 14, 19, 22, 24, 29, 35, 47, 52, 59, 67, 83, 104, 117, 130, 150, 178, 222, 247, 276, 313, 371, 448, 501, 554, 629, 733, 879, 972, 1080, 1214, 1408, 1661, 1837, 2027, 2279, 2613, 3063, 3369, 3718, 4151, 4741
OFFSET
0,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (2=3 := 0 and 0<=1 and 0<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[2] == c[3] == 0 && 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: A117357 A029020 A035380 * A035575 A036816 A367399
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Jean-François Alcover, Oct 11 2024
STATUS
approved