cp's OEIS Frontend

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

%I A025153 #16 Nov 24 2020 16:39:44
%S A025153 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,
%T A025153 14,17,18,21,23,26,29,33,36,41,46,51,57,64,71,79,88,97,109,120,133,
%U A025153 147,164,180,200,220,244,268,297,325,360,395,435,477,526,575,633,693,761,832,913
%N A025153 Number of partitions of n into distinct parts >= 8.
%H A025153 Alois P. Heinz, <a href="/A025153/b025153.txt">Table of n, a(n) for n = 0..1000</a>
%F A025153 a(n) = A026828(n+7). - _R. J. Mathar_, Jul 31 2008
%F A025153 G.f.: Product_{j>=8} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A025153 G.f.: Sum_{k>=0} x^(k*(k + 15)/2) / Product_{j=1..k} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A025153 b:= proc(n, i) option remember;
%p A025153       `if`(n=0, 1, `if`((i-7)*(i+8)/2<n, 0,
%p A025153        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A025153     end:
%p A025153 a:= n-> b(n$2):
%p A025153 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 07 2014
%t A025153 d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 8 &]; Table[d[n], {n, 20}] (* strict partitions, parts >= 8 *)
%t A025153 Table[Length[d[n]], {n, 40}] (* A025153 for n >= 1 *)
%t A025153 (* _Clark Kimberling_, Mar 07 2014 *)
%Y A025153 Cf. A025147.
%K A025153 nonn
%O A025153 0,18
%A A025153 _Clark Kimberling_