OFFSET
0,3
COMMENTS
For example with n=5 neither 32 or 311 are allowed.
Conjecture: Also, for n>=1, a(n-1) is the total number of distinct parts of each partition of 2n with partition rank n. - George Beck, Jun 23 2019
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/E(x) - x*(1-x)/E(x) where E(x) = Product_{k>=1} 1-x^k. [Joerg Arndt, Sep 30 2013]
EXAMPLE
a(2) = 2 : 2, 11.
a(6) = 9 : 6, 51, 411, 33, 3111, 222, 2211, 21111, 111111.
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<t, 0,
b(n, i-1, t)+`if`(i>n, 0, b(n-i, i, t))))
end:
a:= n-> b(n$2, 1)-b((n-1)$2, 2):
seq(a(n), n=0..60); # Alois P. Heinz, Sep 30 2013
MATHEMATICA
nn=50; CoefficientList[Series[ Product[1/(1-x^i), {i, 1, nn}]-x Product[1/(1-x^i), {i, 2, nn}], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 30 2013 *)
Table[PartitionsP[n] - (PartitionsP[n - 1] - PartitionsP[n - 2]), {n, 0, 60}] (* Vincenzo Librandi, Juan 30 2019 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Sep 30 2013
EXTENSIONS
Corrected a(8) and extended beyond a(9), Joerg Arndt, Sep 30 2013
STATUS
approved