cp's OEIS Frontend

A026827 Number of partitions of n into distinct parts, the least being 6.

%I A026827 #24 Nov 25 2020 03:11:25
%S A026827 0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,7,8,9,11,
%T A026827 12,14,16,18,20,23,26,29,33,37,42,47,53,59,67,74,83,93,104,115,129,
%U A026827 143,160,177,197,218,243,268,297,329,364,401,444,489,540,595,655,721,794,872,958
%N A026827 Number of partitions of n into distinct parts, the least being 6.
%H A026827 Alois P. Heinz, <a href="/A026827/b026827.txt">Table of n, a(n) for n = 0..1000</a>
%F A026827 a(n) = A025152(n-6), n>6. - _R. J. Mathar_, Jul 31 2008
%F A026827 G.f.: x^6*Product_{j>=7} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A026827 G.f.: Sum_{k>=1} x^(k*(k + 11)/2) / Product_{j=1..k-1} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A026827 b:= proc(n, i) option remember;
%p A026827       `if`(n=0, 1, `if`((i-6)*(i+7)/2<n, 0,
%p A026827        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A026827     end:
%p A026827 a:= n-> `if`(n<6, 0, b(n-6$2)):
%p A026827 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 07 2014
%t A026827 b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-6)*(i+7)/2 < n, 0, Sum[b[n - i*j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n < 6, 0, b[n-6, n-6]]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jun 24 2015, after _Alois P. Heinz_ *)
%t A026827 Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 6], {n, 66}]] (* _Robert Price_, Jun 13 2020 *)
%Y A026827 Cf. A025147, A025152.
%K A026827 nonn
%O A026827 0,22
%A A026827 _Clark Kimberling_