A026829 Number of partitions of n into distinct parts, the least being 8.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 12, 13, 15, 17, 19, 21, 24, 26, 29, 33, 36, 40, 45, 50, 55, 62, 68, 76, 84, 93, 102, 114, 125, 138, 152, 168, 184, 204, 223, 246, 270, 297, 325, 358, 391, 429, 470

Offset

0,28

Links

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

Formula

a(n) = A025154(n-8), n>8. - R. J. Mathar, Jul 31 2008

G.f.: x^8*Product_{j>=9} (1+x^j). - R. J. Mathar, Jul 31 2008

G.f.: Sum_{k>=1} x^(k*(k + 15)/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-8)*(i+9)/2<n, 0,
       add(b(n-i*j, i-1), j=0..min(1, n/i))))
    end:
a:= n-> `if`(n<8, 0, b(n-8$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-8)*(i+9)/2 < n, 0, Sum[b[n - i*j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n < 8, 0, b[n-8, n-8]]; 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[#] == # &], 8], {n, 66}]] (* Robert Price, Jun 13 2020 *)

Crossrefs

Cf. A025147, A025154.

Sequence in context: A111684 A025159 A264594 * A025154 A241827 A096401

Adjacent sequences: A026826 A026827 A026828 * A026830 A026831 A026832

Keyword

nonn

Author

Clark Kimberling

Status

approved