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A036819
Number of partitions satisfying (cn(0,5) <= cn(1,5) = cn(4,5) and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5)).
0
1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 5, 4, 7, 7, 9, 15, 13, 18, 22, 23, 43, 34, 51, 58, 65, 109, 92, 131, 152, 163, 270, 229, 324, 369, 402, 623, 557, 751, 862, 934, 1399, 1273, 1689, 1919, 2093, 3021, 2818, 3640, 4142, 4505, 6359, 6000, 7640, 8646, 9426
OFFSET
0,7
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (0<=1=4 and 1<=2 and 1<=3).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[1] && c[1] == c[4] &&
c[1] <= c[2] && c[1] <= c[3]];
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: A115000 A036825 A035574 * A351004 A114328 A097366
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Jean-François Alcover, Oct 11 2024
STATUS
approved