cp's OEIS Frontend

A096749 Number of partitions of n into distinct parts, the least being 2.

%I A096749 #39 Nov 24 2020 17:16:15
%S A096749 0,0,1,0,0,1,1,1,1,2,2,3,3,4,5,6,7,9,10,12,15,17,20,24,28,32,38,44,51,
%T A096749 59,68,78,91,103,118,136,155,176,201,228,259,294,332,375,425,478,538,
%U A096749 607,681,764,858,961,1075,1203,1343,1499,1673,1863,2073,2308,2564,2847,3161,3504
%N A096749 Number of partitions of n into distinct parts, the least being 2.
%C A096749 The old entry with this sequence number was a duplicate of A071569.
%C A096749 a(n), n>2 is the Euler transform of [0,0,1,1,1] joined with period [0,1]. - _Georg Fischer_, Aug 15 2020
%H A096749 Alois P. Heinz, <a href="/A096749/b096749.txt">Table of n, a(n) for n = 0..5000</a>
%F A096749 G.f.: x^2*Product_{j>=3} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A096749 a(n) = A025148(n-2), n>1. - _R. J. Mathar_, Sep 30 2008
%F A096749 G.f.: Sum_{k>=1} x^(k*(k + 3)/2) / Product_{j=1..k-1} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A096749 b:= proc(n, i) option remember;
%p A096749       `if`(n=0, 1, `if`((i-2)*(i+3)/2<n, 0,
%p A096749        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A096749     end:
%p A096749 a:= n-> `if`(n<2, 0, b(n-2$2)):
%p A096749 seq(a(n), n=0..60);  # _Alois P. Heinz_, Feb 07 2014
%p A096749 # Using the function EULER from Transforms (see link at the bottom of the page).
%p A096749 [0,0,1,op(EULER([0,0,1,1,seq(irem(n,2),n=1..57)]))]; # _Peter Luschny_, Aug 19 2020
%t A096749 b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-2)*(i+3)/2<n, 0, Sum[b[n-i*j, i-1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n<2, 0, b[n-2, n-2]]; Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Oct 13 2014, after _Alois P. Heinz_ *)
%t A096749 Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 2], {n, 66}]] (* _Robert Price_, Jun 13 2020 *)
%Y A096749 Cf. A025147, A071569.
%Y A096749 Cf. A096765 (least=1), A022824 (3), A022825 (4), A022826 (5), A022827 (6), A022828 (7), A022829 (8), A022830 (9), A022831 (10).
%K A096749 nonn
%O A096749 0,10
%A A096749 _N. J. A. Sloane_, Sep 28 2008