OFFSET
1,2
COMMENTS
If the set mapping has x -> x,2x,x^2 is used instead of x -> x,x+2,2x, the corresponding sequence consists of the Fibonacci numbers 1,2,3,5,8,...
Apparently a(n)= 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4) for n>6, equivalent to a(n)=A000032(n)+n-1 for n>2. - R. J. Mathar, Nov 18 2009
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..43
FORMULA
Empirical g.f.: -x*(x^5-x^4-x^3-x^2+1) / ((x-1)^2*(x^2+x-1)). - Colin Barker, Nov 06 2014
EXAMPLE
Under the indicated set mapping we have {1} -> {1,2,3} -> {1,2,3,4,5,6} -> {1,2,3,4,5,6,7,8,10,12}, ..., so a(2)=3, a(3)=6, a(4)=10, etc.
MATHEMATICA
Do[ Print@ Length@ Nest[ Union@ Flatten[ # /. a_Integer -> {a, 2a, a + 2}] &, {1}, n], {n, 0, 32}] (* Robert G. Wilson v, Sep 27 2006 *)
PROG
(Python)
from sympy import chain, islice
def A122554_gen(): # generator of terms
s = {1}
while True:
yield len(s)
s = set(chain.from_iterable((x, x+2, 2*x) for x in s))
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Sep 20 2006
EXTENSIONS
a(17)-a(33) from Robert G. Wilson v, Sep 27 2006
a(34)-a(36) from Jinyuan Wang, Apr 14 2020
a(37)-a(39) from Chai Wah Wu, Jan 12 2022
STATUS
approved