

A122554


Let S(1) = {1} and, for n>1 let S(n) be the smallest set containing x, 2x and x+2 for each element x in S(n1). a(n) is the number of elements in S(n).


7



1, 3, 6, 10, 15, 23, 35, 54, 84, 132, 209, 333, 533, 856, 1378, 2222, 3587, 5795, 9367, 15146, 24496, 39624, 64101, 103705, 167785, 271468, 439230, 710674, 1149879, 1860527, 3010379, 4870878, 7881228, 12752076, 20633273, 33385317, 54018557, 87403840, 141422362
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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(n1) 2*a(n2) a(n3) +a(n4) for n>6, equivalent to a(n)=A000032(n)+n1 for n>2.  R. J. Mathar, Nov 18 2009


LINKS



FORMULA

Empirical g.f.: x*(x^5x^4x^3x^2+1) / ((x1)^2*(x^2+x1)).  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,more


AUTHOR



EXTENSIONS



STATUS

approved



