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A036808
Number of partitions satisfying (cn(2,5) = cn(3,5) and cn(2,5) <= cn(1,5) and cn(2,5) <= cn(4,5)).
0
1, 1, 1, 1, 2, 3, 4, 4, 5, 7, 11, 13, 15, 17, 23, 34, 40, 44, 52, 67, 98, 111, 124, 143, 184, 257, 290, 321, 372, 467, 640, 715, 793, 911, 1133, 1509, 1684, 1860, 2134, 2617, 3424, 3801, 4202, 4796, 5828, 7484, 8292, 9148, 10419, 12532, 15872, 17529, 19332
OFFSET
0,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (2=3 and 2<=1 and 2<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[2] == c[3] && c[2] <= c[1] && c[2] <= c[4]];
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: A017843 A036815 A036807 * A103750 A036805 A036804
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved