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A039844
Number of partitions satisfying cn(0,5) <= cn(1,5) + cn(4,5) + cn(2,5) and cn(0,5) <= cn(1,5) + cn(4,5) + cn(3,5).
0
1, 1, 2, 3, 5, 6, 11, 14, 21, 29, 40, 53, 74, 96, 129, 170, 221, 284, 370, 469, 605, 761, 964, 1206, 1516, 1890, 2348, 2902, 3586, 4403, 5419, 6611, 8068, 9803, 11906, 14407, 17410, 20946, 25193, 30218, 36205, 43240, 51574, 61363, 72964, 86552, 102534, 121171, 143081, 168652, 198580, 233365, 273885, 320951, 375799
OFFSET
0,3
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: 0 <= 1 + 4 + 2 and 0 <= 1 + 4 + 3 (AApB).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[1] + c[4] + c[2] &&
c[0] <= c[1] + c[4] + 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: A184640 A240490 A039839 * A276107 A187068 A187070
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Jean-François Alcover, Oct 11 2024
STATUS
approved