A036821 Number of partitions satisfying (cn(0,5) = cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 15, 18, 20, 24, 28, 38, 42, 48, 54, 67, 89, 99, 109, 126, 153, 205, 225, 249, 283, 347, 450, 500, 548, 625, 756, 966, 1068, 1178, 1335, 1605, 2004, 2224, 2447, 2777, 3297, 4062, 4496, 4961, 5603, 6606

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 and 0<=1 and 0<=4).

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[2] && c[2] == c[3] &&
   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: A026823 A025148 A096749 * A237980 A026798 A185325

Adjacent sequences: A036818 A036819 A036820 * A036822 A036823 A036824

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved