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A036809
Number of partitions satisfying (cn(0,5) <= cn(1,5) = cn(4,5)).
0
1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 9, 6, 12, 13, 15, 27, 23, 36, 43, 46, 78, 69, 105, 121, 136, 204, 197, 277, 323, 359, 517, 511, 696, 803, 904, 1230, 1265, 1650, 1909, 2145, 2830, 2954, 3771, 4333, 4888, 6253, 6645, 8279, 9505, 10703, 13414, 14384, 17640, 20161
OFFSET
0,6
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (0<=1=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[1] && c[1] == c[4]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 45}] (* Jean-François Alcover, Oct 10 2024 *)
CROSSREFS
Sequence in context: A262699 A153946 A036810 * A111263 A357378 A351257
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved