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A039839
Number of partitions satisfying cn(0,5) <= cn(1,5) + cn(4,5).
0
1, 1, 2, 3, 5, 6, 11, 14, 21, 29, 39, 53, 73, 95, 128, 166, 218, 280, 364, 462, 592, 747, 946, 1184, 1487, 1849, 2299, 2843, 3512, 4310, 5297, 6462, 7891, 9587, 11635, 14073, 16999, 20463, 24610, 29502, 35334, 42191, 50336, 59890, 71182, 84416, 99985, 118185, 139548, 164441, 193573, 227461, 266983, 312864, 366245
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 (AAp).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[1] + c[4]];
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: A238542 A184640 A240490 * A039844 A276107 A187068
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Jean-François Alcover, Oct 11 2024
STATUS
approved