cp's OEIS Frontend

A026826 Number of partitions of n into distinct parts, the least being 5.

%I A026826 #23 Nov 25 2020 03:11:39
%S A026826 0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,7,7,9,10,12,13,
%T A026826 16,17,20,23,26,29,34,38,43,49,55,62,70,79,88,100,111,125,140,157,174,
%U A026826 196,217,243,270,301,333,372,411,457,506,561,619,687,757,837,924,1019,1122
%N A026826 Number of partitions of n into distinct parts, the least being 5.
%H A026826 Alois P. Heinz, <a href="/A026826/b026826.txt">Table of n, a(n) for n = 0..1000</a>
%F A026826 a(n) = A025151(n-5), n>5. - _R. J. Mathar_, Jul 31 2008
%F A026826 G.f.: x^5*Product_{j>=6} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A026826 G.f.: Sum_{k>=1} x^(k*(k + 9)/2) / Product_{j=1..k-1} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A026826 b:= proc(n, i) option remember;
%p A026826       `if`(n=0, 1, `if`((i-5)*(i+6)/2<n, 0,
%p A026826        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A026826     end:
%p A026826 a:= n-> `if`(n<5, 0, b(n-5$2)):
%p A026826 seq(a(n), n=0..80);  # _Alois P. Heinz_, Feb 07 2014
%t A026826 b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-5)*(i+6)/2 < n, 0, Sum[b[n-i*j, i-1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n<5, 0, b[n-5, n-5]]; Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Jun 24 2015, after _Alois P. Heinz_ *)
%t A026826 Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 5], {n, 66}]] (* _Robert Price_, Jun 13 2020 *)
%Y A026826 Cf. A025147, A025151.
%K A026826 nonn,easy
%O A026826 0,19
%A A026826 _Clark Kimberling_