OFFSET
0,4
FORMULA
G.f.: 1 + sum(k>=0, ((x^(k+1)-x)/(x-1))^k ). - Vladeta Jovovic, Sep 24 2004
G.f.: 1 + sum(n>=1, q^n * ( (1-q^n)/(1-q) )^n ), the g.f. above, slightly rewritten. [Joerg Arndt, Mar 30 2014]
a(n) ~ 2^(n-1). - Vaclav Kotesovec, May 01 2014
EXAMPLE
a(5)=11 since 5 can be written as 1+1+1+1+1, 1+1+1+2, 1+1+2+1, 1+1+3, 1+2+1+1, 1+2+2, 1+3+1, 2+1+1+1, 2+1+2, 2+2+1, or 3+1+1; but not as 2+3 since then the largest part (3) would be greater than the number of parts (2).
MATHEMATICA
Table[SeriesCoefficient[1 + Sum[x^k*((1-x^k)/(1-x))^k, {k, 1, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 01 2014 *)
KEYWORD
nonn
AUTHOR
Henry Bottomley, Oct 29 2002
EXTENSIONS
More terms from Vladeta Jovovic, Sep 24 2004
Prepended a(0) = 1, Joerg Arndt, Mar 30 2014
STATUS
approved