login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274142 Number of integers in n-th generation of tree T(1/2) defined in Comments. 30
1, 1, 1, 2, 2, 4, 5, 8, 11, 17, 25, 37, 54, 81, 119, 177, 261, 388, 574, 851, 1260, 1868, 2767, 4101, 6077, 9006, 13347, 19781, 29315, 43448, 64392, 95436, 141444, 209636, 310705, 460501, 682519, 1011581, 1499295, 2222155, 3293534, 4881472, 7235018, 10723311, 15893460, 23556367, 34913897, 51747400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Let T* be the infinite tree with root 0 generated by these rules:  if p is in T*, then p+1 is in T* and x*p is in T*.  Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc.  Let T(r) be the tree obtained by substituting r for x.

Guide to related sequences:

r           sequence

1/2         A274142

1/3         A274143

1/4         A274144

2/3         A274145

3/4         A274146

-1/2        A274147

-1/3        A274148

-1/4        A274149

-2/3        A274150

-3/4        A274151

3/2         A274152

5/2         A274153

-3/2        A274154

-5/2        A274155

2^(1/2)     A000045 (Fibonacci numbers)

2^(1/3)     A000930

2^(1/4)     A003269

2^(-1/2)    A274156

3^(-1/2)    A274157

2^(-1/3)    A274158

3^(-1/3)    A274159

i           A274160

2i          A206743

3i          A274162

4i          A274163

i/2         A274149

i/3         A274165

i+1         A274166

i-1         A274167

(-1+3i)/2   A274168

LINKS

Kenny Lau, Table of n, a(n) for n = 0..5847

EXAMPLE

If r = 1/2, then g(3) = {3,2r,r+1, r^2}, in which the integers are 3 and 1, so that a(3) = 2.

MATHEMATICA

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];

u = Table[t[[k]] /. x -> 1/2, {k, 1, z}];

Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

(* second program: *)

T[0] = {0}; T[n_] := T[n] = Complement[Join[T[n-1]+1, x*T[n-1]], T[n-1]]; Reap[For[n = 0, n <= 25, n++, cnt = Count[T[n] /. x -> 1/2, _Integer]; Print[n, " ", cnt]; Sow[cnt]]][[2, 1]] (* Jean-François Alcover, Jun 14 2016 *)

CROSSREFS

Cf. A274143-A274160, A274162, A274163, A274165-A274168.

Sequence in context: A238478 A013979 A107458 * A060280 A006206 A095719

Adjacent sequences:  A274139 A274140 A274141 * A274143 A274144 A274145

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 11 2016

EXTENSIONS

More terms from Jean-François Alcover, Jun 14 2016

More terms from Kenny Lau, Jul 04 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 24 15:07 EDT 2017. Contains 288697 sequences.