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A240538
Number of partitions p of n such that the m(M(p)) is a part, where m = multiplicity, M = the maximum multiplicity of the parts of p.
2
0, 1, 0, 1, 3, 2, 4, 4, 8, 9, 17, 19, 26, 32, 47, 54, 81, 96, 126, 161, 210, 249, 331, 407, 514, 630, 794, 962, 1206, 1467, 1803, 2197, 2694, 3235, 3961, 4761, 5762, 6914, 8338, 9951, 11954, 14232, 16990, 20188, 24028, 28407, 33713, 39786, 46996, 55329
OFFSET
0,5
EXAMPLE
a(6) counts these 4 partitions: 51, 321, 3111, 2211; e.g., the multiplicities of the parts of p = {2,2,1,1| are 2 and 2, of which the max is 2, and the multiplicity of 2 in p is 2, which is a part of p.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n]; m1[p_] := Max[Map[Length, Split[p]]]; m2[p_] := Min[Map[Length, Split[p]]];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, m1[p]]]], {n, 0, z}] (* A240538 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, m2[p]]]], {n, 0, z}] (* A240539 *)
CROSSREFS
Cf. A240539.
Sequence in context: A309511 A195472 A370806 * A326923 A365613 A338315
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 07 2014
STATUS
approved