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 A240201 Number of partitions p of n such that mean(p) <= multiplicity(max(p)). 3
 0, 1, 1, 1, 2, 2, 3, 3, 5, 6, 8, 9, 13, 14, 19, 22, 29, 33, 44, 47, 63, 71, 87, 100, 130, 138, 175, 202, 242, 272, 340, 365, 460, 516, 601, 687, 847, 891, 1095, 1249, 1440, 1600, 1943, 2085, 2529, 2816, 3185, 3621, 4356, 4555, 5456, 6166, 6952, 7691, 9156 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Table of n, a(n) for n=0..54. FORMULA a(n) = A240201(n) + A116900(n) for n >= 1. a(n) + A240202(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 3 partitions: 222, 2211, 111111. MATHEMATICA z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Max[p]]], {n, 0, z}] (* A240200 *) t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240201 *) t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Max[p]]], {n, 0, z}] (* A116900 *) t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Max[p]]], {n, 0, z}] (* A240202 *) t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Max[p]]], {n, 0, z}] (* A116901 *) CROSSREFS Cf. A240200, A240202, A116900, A116901, A000041. Sequence in context: A035577 A002723 A035937 * A274158 A020999 A309712 Adjacent sequences: A240198 A240199 A240200 * A240202 A240203 A240204 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 03 2014 STATUS approved

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Last modified December 3 19:10 EST 2023. Contains 367540 sequences. (Running on oeis4.)