A025154 Number of partitions of n into distinct parts >= 9.

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, 515, 562, 616, 672, 735

Offset

0,20

Links

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

Formula

a(n) = A026829(n+8). - R. J. Mathar, Jul 31 2008

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

G.f.: Sum_{k>=0} x^(k*(k + 17)/2) / Product_{j=1..k} (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-> b(n$2):
seq(a(n), n=0..100);  # Alois P. Heinz, Feb 07 2014

Mathematica

d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 9 &]; Table[d[n], {n, 25}] (* strict partitions, parts >= 9 *)
Table[Length[d[n]], {n, 40}] (* A025154 for n >= 1 *)
(* Clark Kimberling, Mar 07 2014 *)

Crossrefs

Cf. A025147.

Sequence in context: A025159 A264594 A026829 * A241827 A096401 A264593

Adjacent sequences: A025151 A025152 A025153 * A025155 A025156 A025157

Keyword

nonn

Author

Clark Kimberling

Status

approved