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 A240302 Number of partitions of n such that (maximal multiplicity of parts) > (multiplicity of the maximal part). 2
 0, 0, 0, 0, 1, 2, 3, 7, 10, 16, 23, 35, 47, 70, 93, 126, 169, 228, 294, 391, 501, 648, 827, 1057, 1329, 1683, 2105, 2631, 3266, 4056, 4992, 6156, 7538, 9221, 11234, 13664, 16549, 20033, 24152, 29077, 34904, 41844, 50012, 59710, 71100, 84541, 100318, 118869 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) + A171979(n) = A000041(n) for n >= 1. EXAMPLE a(7) counts these 7 partitions: 511, 4111, 322, 3211, 31111, 22111, 211111. MAPLE b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0),       `if`(i<1, 0, b(n, i-1, k) +add(b(n-i*j, i-1, `if`(k=-1, j,       `if`(k=0, 0, `if`(j>k, 0, k)))), j=1..n/i)))     end: a:= n-> b(n\$2, -1): seq(a(n), n=0..70);  # Alois P. Heinz, Apr 12 2014 MATHEMATICA z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]] (* maximal multiplicity *) Table[Count[f[n], p_ /; m[p] == Count[p, Max[p]]], {n, 0, z}] (* A171979 *) Table[Count[f[n], p_ /; m[p] > Count[p, Max[p]]], {n, 0, z}] (* A240302 *) CROSSREFS Cf. A240221, A000041. Sequence in context: A192116 A088163 A048448 * A281611 A054060 A024832 Adjacent sequences:  A240299 A240300 A240301 * A240303 A240304 A240305 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 04 2014 STATUS approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)