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A240497
Number of partitions p of n such that the multiplicity of (min(p) + max(p))/2 is a part.
5
1, 0, 0, 1, 0, 1, 1, 2, 5, 5, 7, 10, 12, 17, 23, 30, 35, 49, 61, 78, 97, 124, 155, 200, 243, 307, 375, 470, 568, 710, 857, 1051, 1269, 1554, 1862, 2265, 2700, 3273, 3895, 4685, 5558, 6658, 7883, 9394, 11084, 13167, 15493, 18336, 21517, 25367, 29703, 34914
OFFSET
1,8
EXAMPLE
a(9) counts these 5 partitions: 531, 333, 3321, 32211, 321111.
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
AUTHOR
Clark Kimberling, Apr 06 2014
STATUS
approved