

A168043


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


3



1, 2, 4, 7, 13, 23, 40, 68, 114, 189, 311, 509, 830, 1350, 2192, 3555, 5761, 9331, 15108, 24456, 39582, 64057, 103659, 167737, 271418, 439178, 710620, 1149823, 1860469, 3010319, 4870816, 7881164, 12752010, 20633205, 33385247
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Table of n, a(n) for n=1..35.


FORMULA

It appears that a(n) = a(n1) + a(n2) + n  3, for n>3.
From R. J. Mathar, Nov 18 2009: (Start)
Apparently: a(n) = 3*a(n1)  2*a(n2)  a(n3) + a(n4) for n>5;
and a(n) = A000032(n+1)  n for n>1. (End)
From Ilya Gutkovskiy, Jul 07 2016: (Start)
It appears that the g.f. is x*(1  x + x^4)/((1  x)^2*(1  x  x^2)); and the e.g.f. is phi*exp(phi*x)  exp(x/phi)/phi  x*(1 + exp(x))  1, where phi is the golden ratio. (End)
It would be nice to have a proof for any one of these formulas. The others would then presumably follow easily.  N. J. A. Sloane, Jul 11 2016


EXAMPLE

Under the indicated set mapping we have {1} > {2,3} > {3,4,5,6} > {4,5,6,7,8,10,12}, ..., so a(2)=2, a(3)=4, a(4)=7, etc.


CROSSREFS

Cf. A000032, A122554.
Sequence in context: A051013 A128609 A335471 * A114832 A239553 A319255
Adjacent sequences: A168040 A168041 A168042 * A168044 A168045 A168046


KEYWORD

nonn,more


AUTHOR

John W. Layman, Nov 17 2009


EXTENSIONS

6 more terms from R. J. Mathar, Nov 18 2009
a(23)a(35) from Jinyuan Wang, Apr 14 2020


STATUS

approved



