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A036811
Number of partitions satisfying (cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5) 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, 8, 9, 11, 12, 16, 26, 29, 31, 37, 48, 76, 82, 90, 103, 136, 199, 218, 237, 274, 349, 495, 542, 593, 679, 855, 1165, 1281, 1399, 1602, 1981, 2642, 2893, 3172, 3613, 4420, 5770, 6313, 6913, 7862, 9505, 12234, 13345, 14619, 16558
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 and 0<=1 and 0<=4 and 2<=1 and 2<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[2] == c[3] && c[0] <= c[1] &&
c[0] <= c[4] && 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, 1, 45}] (* Jean-François Alcover, Oct 10 2024 *)
CROSSREFS
Sequence in context: A147663 A301765 A374210 * A330265 A302163 A302635
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved