OFFSET
0,10
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
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
MAPLE
b:= proc(n, i) option remember;
`if`(n=0, 1, `if`((i-2)*(i+3)/2<n, 0,
add(b(n-i*j, i-1), j=0..min(1, n/i))))
end:
a:= n-> `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)/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 *)
Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 2], {n, 66}]] (* Robert Price, Jun 13 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 28 2008
STATUS
approved