cp's OEIS Frontend

A026830 Number of partitions of n into distinct parts, the least being 9.

%I A026830 #20 Nov 25 2020 07:42:48
%S A026830 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,
%T A026830 4,4,5,5,6,6,7,7,9,9,11,12,14,15,18,19,22,24,27,29,33,36,40,44,49,54,
%U A026830 60,66,73,81,89,98,108,119,130,144,157,173,189,208,227,250,272,299,326,358,389
%N A026830 Number of partitions of n into distinct parts, the least being 9.
%H A026830 Alois P. Heinz, <a href="/A026830/b026830.txt">Table of n, a(n) for n = 0..1000</a>
%F A026830 a(n) = A025155(n-9), n>9. - _R. J. Mathar_, Jul 31 2008
%F A026830 G.f.: x^9*Product_{j>=10} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A026830 G.f.: Sum_{k>=1} x^(k*(k + 17)/2) / Product_{j=1..k-1} (1 - x^j). - _Ilya Gutkovskiy_, Nov 25 2020
%p A026830 b:= proc(n, i) option remember;
%p A026830       `if`(n=0, 1, `if`((i-9)*(i+10)/2<n, 0,
%p A026830        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A026830     end:
%p A026830 a:= n-> `if`(n<9, 0, b(n-9$2)):
%p A026830 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 07 2014
%t A026830 dp9[n_]:=Module[{ips=IntegerPartitions[n]},Length[Select[ips,Min[#] == 9 && Length[#]==Length[Union[#]]&]]]; Table[dp9[n],{n,0,80}] (* _Harvey P. Dale_, Oct 23 2015 *)
%t A026830 Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 9], {n, 66}]] (* _Robert Price_, Jun 13 2020 *)
%Y A026830 Cf. A025147, A025155.
%K A026830 nonn
%O A026830 0,31
%A A026830 _Clark Kimberling_