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A239950 Number of partitions of n such that (number of distinct parts) = least part. 5
0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 6, 6, 9, 8, 14, 11, 19, 18, 25, 24, 37, 31, 50, 46, 61, 64, 86, 79, 112, 115, 136, 149, 190, 184, 239, 255, 293, 329, 382, 408, 489, 531, 595, 675, 772, 827, 952, 1066, 1176, 1320, 1468, 1627, 1827, 2030, 2219, 2493, 2769, 3053 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Also for n>0 the number of partitions of n such that (number of distinct parts) = multiplicity of the greatest part (by conjugation of the partition table). - Joerg Arndt, Apr 28 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

A239948(n) + a(n) + A239951(n) = A000041(n) for n >= 0.

EXAMPLE

a(8) counts these 4 partitions :  62, 422, 332, 11111111.

MAPLE

b:= proc(n, i, d) option remember; `if`(min(i, n)<d+1, 0,

      `if`(irem(n, i)=0 and i=d+1, 1, b(n, i-1, d)+

      add(b(n-i*j, i-1, d+1), j=1..n/i)))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..60);  # 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[Min[i, n]<d+1, 0, If[Mod[n, i]==0 && i == d+1, 1, b[n, i-1, d] + Sum[b[n-i*j, i-1, d+1], {j, 1, n/i}]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 60}] (* Jean-Fran├žois Alcover, Nov 17 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A239948, A239949, A239951, A239952.

Sequence in context: A138374 A029936 A114093 * A077768 A143038 A029040

Adjacent sequences:  A239947 A239948 A239949 * A239951 A239952 A239953

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 30 2014

STATUS

approved

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Last modified August 11 03:22 EDT 2020. Contains 336421 sequences. (Running on oeis4.)