cp's OEIS Frontend

A026828 Number of partitions of n into distinct parts, the least being 7.

%I A026828 #23 Nov 25 2020 03:10:46
%S A026828 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,
%T A026828 8,8,10,11,13,14,17,18,21,23,26,29,33,36,41,46,51,57,64,71,79,88,97,
%U A026828 109,120,133,147,164,180,200,220,244,268,297,325,360,395,435,477,526,575,633,693
%N A026828 Number of partitions of n into distinct parts, the least being 7.
%H A026828 Alois P. Heinz, <a href="/A026828/b026828.txt">Table of n, a(n) for n = 0..1000</a>
%F A026828 a(n) = A025153(n-7), n>7. - _R. J. Mathar_, Jul 31 2008
%F A026828 G.f.: x^7*Product_{j>=8} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A026828 G.f.: Sum_{k>=1} x^(k*(k + 13)/2) / Product_{j=1..k-1} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A026828 b:= proc(n, i) option remember;
%p A026828       `if`(n=0, 1, `if`((i-7)*(i+8)/2<n, 0,
%p A026828        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A026828     end:
%p A026828 a:= n-> `if`(n<7, 0, b(n-7$2)):
%p A026828 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 07 2014
%t A026828 b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-7)*(i+8)/2 < n, 0, Sum[b[n - i*j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n < 7, 0, b[n-7, n-7]]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jun 24 2015, after _Alois P. Heinz_ *)
%t A026828 Join[{0}, Table[Count[ Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 7], {n, 66}]] (* _Robert Price_, Jun 13 2020 *)
%Y A026828 Cf. A025147, A025153.
%K A026828 nonn
%O A026828 0,25
%A A026828 _Clark Kimberling_