A026827 Number of partitions of n into distinct parts, the least being 6.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 11, 12, 14, 16, 18, 20, 23, 26, 29, 33, 37, 42, 47, 53, 59, 67, 74, 83, 93, 104, 115, 129, 143, 160, 177, 197, 218, 243, 268, 297, 329, 364, 401, 444, 489, 540, 595, 655, 721, 794, 872, 958

Offset

0,22

Links

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

Formula

a(n) = A025152(n-6), n>6. - R. J. Mathar, Jul 31 2008

G.f.: x^6*Product_{j>=7} (1+x^j). - R. J. Mathar, Jul 31 2008

G.f.: Sum_{k>=1} x^(k*(k + 11)/2) / Product_{j=1..k-1} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, `if`((i-6)*(i+7)/2<n, 0,
       add(b(n-i*j, i-1), j=0..min(1, n/i))))
    end:
a:= n-> `if`(n<6, 0, b(n-6$2)):
seq(a(n), n=0..100);  # Alois P. Heinz, Feb 07 2014

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-6)*(i+7)/2 < n, 0, Sum[b[n - i*j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n < 6, 0, b[n-6, n-6]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *)
Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 6], {n, 66}]] (* Robert Price, Jun 13 2020 *)

Crossrefs

Cf. A025147, A025152.

Sequence in context: A025158 A179046 A264592 * A025152 A026802 A185329

Adjacent sequences: A026824 A026825 A026826 * A026828 A026829 A026830

Keyword

nonn

Author

Clark Kimberling

Status

approved