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A036816
Number of partitions satisfying (cn(0,5) <= cn(2,5) = cn(3,5) and cn(2,5) <= cn(1,5) and cn(2,5) <= cn(4,5)).
0
1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7, 8, 10, 11, 14, 21, 24, 26, 31, 39, 60, 65, 72, 82, 107, 155, 170, 185, 214, 271, 383, 419, 459, 525, 660, 896, 987, 1078, 1234, 1524, 2024, 2221, 2437, 2775, 3391, 4403, 4832, 5296, 6024, 7271, 9304, 10180, 11168, 12650, 15146
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 2<=1 and 2<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[2] && c[2] == c[3] &&
c[2] <= c[1] && c[2] <= 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: A035380 A036823 A035575 * A367399 A113788 A018243
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Jean-François Alcover, Oct 11 2024
STATUS
approved