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A239949 Number of partitions of n such that (number of distinct parts) <= least part. 5
1, 1, 2, 2, 3, 3, 5, 5, 8, 8, 12, 12, 18, 17, 26, 25, 36, 36, 50, 50, 69, 69, 93, 95, 123, 129, 164, 171, 215, 229, 278, 300, 365, 387, 468, 507, 595, 652, 760, 830, 966, 1055, 1214, 1336, 1530, 1674, 1910, 2104, 2380, 2617, 2953, 3253, 3656, 4019, 4504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

EXAMPLE

a(8) counts these 8 partitions:  8, 62, 53, 44, 422, 332, 2222, 11111111.

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-> 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_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, Nov 17 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A239948, A239950, A239951, A239952.

Sequence in context: A275972 A090492 A325768 * A103609 A237800 A232697

Adjacent sequences:  A239946 A239947 A239948 * A239950 A239951 A239952

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 30 2014

STATUS

approved

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)