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 A240206 Number of partitions p of n such that mean(p) > multiplicity(min(p)). 5
 0, 0, 1, 2, 2, 4, 5, 9, 11, 16, 22, 31, 39, 56, 71, 91, 123, 157, 195, 263, 324, 405, 529, 649, 790, 1032, 1253, 1514, 1902, 2357, 2826, 3497, 4179, 5153, 6279, 7459, 8880, 11079, 13089, 15435, 18438, 22596, 26514, 31423, 36783, 44336, 52827, 61570, 71653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..48. FORMULA a(n) = A240079(n) - A240205(n) for n >= 0. a(n) + A240203(n) + A240205(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 5 partitions: 6, 51, 42, 33, 321. MATHEMATICA z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}] (* A240203 *) t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *) t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *) t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *) t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *) CROSSREFS Cf. A240203, A240204, A240205, A240079, A000041. Sequence in context: A326447 A326527 A326632 * A229816 A099574 A144118 Adjacent sequences: A240203 A240204 A240205 * A240207 A240208 A240209 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 03 2014 STATUS approved

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Last modified November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)