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A036802
Number of partitions satisfying (cn(2,5) <= cn(1,5) and cn(3,5) <= cn(1,5) and cn(2,5) <= cn(4,5) and cn(3,5) <= cn(4,5)).
0
1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 13, 16, 23, 29, 36, 48, 60, 80, 102, 123, 160, 195, 253, 312, 380, 476, 577, 723, 885, 1065, 1313, 1574, 1935, 2331, 2795, 3383, 4036, 4871, 5818, 6918, 8282, 9800, 11695, 13832, 16352, 19362, 22783, 26901, 31608, 37101, 43580, 50962
OFFSET
0,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (2<=1 and 3<=1 and 2<=4 and 3<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[2] <= c[1] && c[3] <= c[1] &&
c[2] <= c[4] && c[3] <= 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: A280451 A240178 A039863 * A333265 A055167 A064628
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved