OFFSET
4,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 4..1000
FORMULA
a(n) ~ 1/sqrt(5) * ((1+sqrt(5))/2)^(n+1). - Vaclav Kotesovec, Aug 21 2014
EXAMPLE
a(4) = 3: [2,1,1], [1,2,1], [1,1,2].
a(5) = 10: [2,1,1,1], [1,2,1,1], [1,1,2,1], [1,1,1,2], [2,2,1], [2,1,2], [1,2,2], [3,1,1], [1,3,1], [1,1,3].
MAPLE
with(numtheory):
a:= n-> add(add(add(`if`(d<p and (n-p*m)/d<>m, binomial((n-p*m)
/d+m, m), 0), d=divisors(n-p*m)), m=1..n/p), p=2..n-1):
seq(a(n), n=4..60);
MATHEMATICA
div[0] = {}; div[n_] := Divisors[n]; a[n_] := Sum[Sum[Sum[If[d<p && (n-p*m)/d != m, Binomial[(n-p*m)/d+m, m], 0], {d, div[n-p*m]}], {m, 1, n/p}], {p, 2, n-1}]; Table[ a[n], {n, 4, 60}] (* Jean-François Alcover, Feb 11 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 25 2014
STATUS
approved