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A036810
Number of partitions satisfying (cn(1,5) = cn(4,5) and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5)).
0
1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 9, 6, 12, 13, 15, 27, 23, 35, 42, 45, 78, 67, 101, 116, 130, 203, 187, 262, 305, 336, 511, 475, 652, 749, 833, 1206, 1159, 1530, 1763, 1951, 2754, 2672, 3472, 3969, 4403, 6039, 5957, 7570, 8649, 9564, 12866, 12796, 16044, 18241
OFFSET
0,6
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (1=4 and 0<=2 and 0<=3).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[1] == c[4] && c[0] <= c[2] && c[0] <= c[3]];
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: A137776 A262699 A153946 * A036809 A111263 A357378
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved