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 A239951 Number of partitions of n such that (number of distinct parts) > least part. 5
 0, 0, 0, 1, 2, 4, 6, 10, 14, 22, 30, 44, 59, 84, 109, 151, 195, 261, 335, 440, 558, 723, 909, 1160, 1452, 1829, 2272, 2839, 3503, 4336, 5326, 6542, 7984, 9756, 11842, 14376, 17382, 20985, 25255, 30355, 36372, 43528, 51960, 61925, 73645, 87460, 103648, 122650 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) + A239949(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 6 partitions:  51, 411, 321, 3111, 2211, 21111. MAPLE b:= proc(n, i, d) option remember; `if`(n=0, 1, `if`(i<=d, 0,       add(b(n-i*j, i-1, d+`if`(j=0, 0, 1)), j=0..n/i)))     end: a:= n-> combinat[numbpart](n) -b(n\$2, 0): seq(a(n), n=0..80);  # Alois P. Heinz, Apr 02 2014 MATHEMATICA z = 50; d[p_] := d[p] = Length[DeleteDuplicates[p]]; f[n_] := f[n] = IntegerPartitions[n]; Table[Count[f[n], p_ /; d[p] < Min[p]], {n, 0, z}]  (*A239948*) Table[Count[f[n], p_ /; d[p] <= Min[p]], {n, 0, z}] (*A239949*) Table[Count[f[n], p_ /; d[p] == Min[p]], {n, 0, z}] (*A239950*) Table[Count[f[n], p_ /; d[p] > Min[p]], {n, 0, z}]  (*A239951*) Table[Count[f[n], p_ /; d[p] >= Min[p]], {n, 0, z}] (*A239952*) b[n_, i_, d_] := b[n, i, d] = If[n==0, 1, If[i<=d, 0, Sum[b[n-i*j, i-1, d + If[j==0, 0, 1]], {j, 0, n/i}]]]; a[n_] := PartitionsP[n] - b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Nov 17 2015, after Alois P. Heinz *) CROSSREFS Cf. A239948, A239949, A239950, A239952. Sequence in context: A103445 A001747 A048670 * A077625 A027383 A280611 Adjacent sequences:  A239948 A239949 A239950 * A239952 A239953 A239954 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 30 2014 STATUS approved

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Last modified October 20 19:40 EDT 2018. Contains 316401 sequences. (Running on oeis4.)