cp's OEIS Frontend

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

%I A025152 #14 Nov 24 2020 10:23:59
%S A025152 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,
%T A025152 20,23,26,29,33,37,42,47,53,59,67,74,83,93,104,115,129,143,160,177,
%U A025152 197,218,243,268,297,329,364,401,444,489,540,595,655,721,794,872,958,1053,1156
%N A025152 Number of partitions of n into distinct parts >= 7.
%H A025152 Alois P. Heinz, <a href="/A025152/b025152.txt">Table of n, a(n) for n = 0..1000</a>
%F A025152 a(n) = A026827(n+6). - _R. J. Mathar_, Jul 31 2008
%F A025152 G.f.: product_{j=7..infinity} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A025152 G.f.: Sum_{k>=0} x^(k*(k + 13)/2) / Product_{j=1..k} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A025152 b:= proc(n, i) option remember;
%p A025152       `if`(n=0, 1, `if`((i-6)*(i+7)/2<n, 0,
%p A025152        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A025152     end:
%p A025152 a:= n-> b(n$2):
%p A025152 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 07 2014
%t A025152 d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 7 &]; Table[d[n], {n, 20}] (* strict partitions, parts >= 7 *)
%t A025152 Table[Length[d[n]], {n, 40}] (* A025152 for n >= 1 *)
%t A025152 (* _Clark Kimberling_, Mar 07 2014 *)
%Y A025152 Cf. A025147.
%K A025152 nonn
%O A025152 0,16
%A A025152 _Clark Kimberling_