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A277753
Number of partitions p of n that contain a proper partition of the number of parts of p.
0
0, 0, 0, 0, 1, 2, 4, 8, 12, 19, 28, 42, 58, 82, 110, 150, 200, 263, 344, 450, 578, 741, 947, 1197, 1513, 1899, 2374, 2954, 3669, 4529, 5576, 6849, 8380, 10223, 12449
OFFSET
1,6
EXAMPLE
a(9) counts these 12 partitions: [6,2,1], [5,2,1,1], [4,3,1,1], [4,2,2,1], [4,2,1,1,1], [3,3,1,1,1], [3,2,2,2], [3,2,2,1,1], [3,2,1,1,1,1], [2,2,2,2,1], [2,2,2,1,1,1],[2,2,1,1,1,1,1]; e.g., [2,2,1] is a proper partition of 5, which is the number of parts in [3,2,2,1,1].
MATHEMATICA
Table[parts = IntegerPartitions[z];
Count[Table[rest = Rest[parts[[nn]]];
seq = Map[{#, Flatten[{___, #, ___}]} &,
Rest[IntegerPartitions[Length[rest] + 1]]];
Apply[Or, Map[MatchQ[rest, #[[2]]] &, seq]], {nn, Length[parts]}],
True], {z, 30}] (* Peter J. C. Moses, Dec 06 2016 *)
CROSSREFS
Cf. A000041.
Sequence in context: A136184 A011908 A117455 * A237820 A110571 A037168
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 07 2016
STATUS
approved