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A240498
Number of partitions p of n such that the multiplicity of min(p)*max(p) is a part.
5
0, 1, 0, 1, 2, 4, 6, 8, 12, 17, 25, 35, 48, 65, 88, 116, 154, 203, 263, 342, 440, 562, 716, 908, 1141, 1436, 1794, 2234, 2771, 3431, 4223, 5194, 6359, 7770, 9462, 11502, 13929, 16852, 20318, 24458, 29364, 35204, 42088, 50257, 59865, 71212, 84531, 100208
OFFSET
0,5
EXAMPLE
a(6) counts these 6 partitions: 51, 411, 3111, 21111, 321.
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