

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).


5



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
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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

Table of n, a(n) for n=1..36.


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 *)


CROSSREFS

Sequence in context: A262927 A063542 A294413 * A111734 A117457 A024674
Adjacent sequences: A122551 A122552 A122553 * A122555 A122556 A122557


KEYWORD

nonn,more


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


STATUS

approved



