A025153 Number of partitions of n into distinct parts >= 8.

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 14, 17, 18, 21, 23, 26, 29, 33, 36, 41, 46, 51, 57, 64, 71, 79, 88, 97, 109, 120, 133, 147, 164, 180, 200, 220, 244, 268, 297, 325, 360, 395, 435, 477, 526, 575, 633, 693, 761, 832, 913

Offset

0,18

Links

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

Formula

a(n) = A026828(n+7). - R. J. Mathar, Jul 31 2008

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

G.f.: Sum_{k>=0} x^(k*(k + 15)/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-7)*(i+8)/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[#] >= 8 &]; Table[d[n], {n, 20}] (* strict partitions, parts >= 8 *)
Table[Length[d[n]], {n, 40}] (* A025153 for n >= 1 *)
(* Clark Kimberling, Mar 07 2014 *)

Crossrefs

Cf. A025147.

Sequence in context: A096401 A264593 A026828 * A026803 A286041 A027192

Adjacent sequences: A025150 A025151 A025152 * A025154 A025155 A025156

Keyword

nonn

Author

Clark Kimberling

Status

approved