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A036825
Number of partitions satisfying (cn(1,5) = cn(4,5) = 0 and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5)).
0
1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 5, 4, 7, 7, 9, 13, 13, 16, 20, 21, 32, 30, 40, 45, 52, 69, 70, 87, 101, 110, 149, 147, 185, 208, 232, 296, 306, 366, 418, 459, 581, 594, 715, 800, 886, 1091, 1135, 1332, 1501, 1644, 2012, 2086, 2442, 2721, 2994
OFFSET
0,7
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (1=4 := 0 and 0<=2 and 0<=3).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[1] == c[4] == 0 &&
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, 0, 54}] (* Jean-François Alcover, Oct 11 2024 *)
CROSSREFS
Sequence in context: A194451 A059292 A115000 * A035574 A036819 A351004
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Jean-François Alcover, Oct 11 2024
STATUS
approved