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A240500
Number of partitions of n such that the multiplicity of 2*(number of parts) is a part.
5
0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 2, 2, 5, 5, 6, 9, 9, 13, 17, 21, 25, 32, 39, 48, 59, 73, 87, 109, 129, 156, 190, 226, 271, 328, 388, 463, 552, 654, 772, 919, 1078, 1271, 1500, 1760, 2059, 2418, 2820, 3296, 3844, 4475, 5198, 6048, 7006, 8121, 9400, 10866
OFFSET
0,12
EXAMPLE
a(14) counts these 5 partitions: [10,1,1,1,1], [8,4,1,1], [8,3,2,1], [7,6,1], [6,6,2].
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Min[p]]]], {n, 0, z}] (* A240496 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, (Min[p] + Max[p])/2]]], {n, 1, z}] (* A240497 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]*Max[p]]]], {n, 0, z}] (* A240498 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Length[p]]]], {n, 0, z}] (* A240499 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Length[p]]]], {n, 0, z}] (* A240500 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Clark Kimberling, Apr 06 2014
STATUS
approved