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

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, 59, 68, 78, 91, 103, 118, 136, 155, 176, 201, 228, 259, 294, 332, 375, 425, 478, 538, 607, 681, 764, 858, 961, 1075, 1203, 1343, 1499, 1673, 1863, 2073, 2308, 2564, 2847, 3161, 3504

Offset: 0

Author

N. J. A. Sloane, Sep 28 2008

Keywords

• nonn

Comments

The old entry with this sequence number was a duplicate of A071569.

a(n), n>2 is the Euler transform of [0,0,1,1,1] joined with period [0,1]. - Georg Fischer, Aug 15 2020

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A025147, A071569.

Cf. A096765 (least=1), A022824 (3), A022825 (4), A022826 (5), A022827 (6), A022828 (7), A022829 (8), A022830 (9), A022831 (10).

Programs

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, `if`((i-2)*(i+3)/2 `if`(n<2, 0, b(n-2$2)):
seq(a(n), n=0..60);  # Alois P. Heinz, Feb 07 2014
# Using the function EULER from Transforms (see link at the bottom of the page).
[0,0,1,op(EULER([0,0,1,1,seq(irem(n,2),n=1..57)]))]; # Peter Luschny, Aug 19 2020

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-2)*(i+3)/2Jean-François Alcover, Oct 13 2014, after Alois P. Heinz *)
Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 2], {n, 66}]] (* Robert Price, Jun 13 2020 *)

Formula

G.f.: x^2*Product_{j>=3} (1+x^j). - R. J. Mathar, Jul 31 2008

a(n) = A025148(n-2), n>1. - R. J. Mathar, Sep 30 2008

G.f.: Sum_{k>=1} x^(k*(k + 3)/2) / Product_{j=1..k-1} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020