A025152 Number of partitions of n into distinct parts >= 7.

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, 1053, 1156

Offset

0,16

Links

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

Formula

a(n) = A026827(n+6). - R. J. Mathar, Jul 31 2008

G.f.: product_{j=7..infinity} (1+x^j). - R. J. Mathar, Jul 31 2008

G.f.: Sum_{k>=0} x^(k*(k + 13)/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-6)*(i+7)/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[#] >= 7 &]; Table[d[n], {n, 20}] (* strict partitions, parts >= 7 *)
Table[Length[d[n]], {n, 40}] (* A025152 for n >= 1 *)
(* Clark Kimberling, Mar 07 2014 *)

Crossrefs

Cf. A025147.

Sequence in context: A179046 A264592 A026827 * A026802 A185329 A029031

Adjacent sequences: A025149 A025150 A025151 * A025153 A025154 A025155

Keyword

nonn

Author

Clark Kimberling

Status

approved