OFFSET
1,1
COMMENTS
This is one of three sequences that partition the positive integers.
Given t is the tribonacci constant, then the following sequences are disjoint:
. A184820(n) = n + [n/t] + [n/t^2],
. A184821(n) = n + [n*t] + [n/t],
. A184822(n) = n + [n*t] + [n*t^2], where []=floor.
This is a special case of Clark Kimberling's results given in A184812.
FORMULA
Limit a(n)/n = t^2 = 3.3829757679...
a(n) = n + floor(n*p/q) + floor(n*r/q), where p=t, q=t^2, r=t^3, and t is the tribonacci constant (see Clark Kimberling's formula in A184812).
EXAMPLE
Let t be the tribonacci constant, then t^2 = 1 + t + 1/t where:
t = 1.8392867552..., t^2 = 3.3829757679..., t^3 = 6.2222625231...
PROG
(PARI) {a(n)=local(t=real(polroots(1+x+x^2-x^3)[1])); n+floor(n*t)+floor(n/t)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 22 2011
STATUS
approved