login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114730 One of a family of fractal sequences that transforms into each other. 6
1, 1, 2, 2, 1, 1, 1, 2, 3, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5, 6, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Let A be the sequence A114729 (1, 1, 1, 2, 3, 2, 2, 1, 1, 1, ...), B be the sequence A114730 (1, 1, 2, 2, 1, 1, 1, 2, 3, 4, ...) and C be the sequence A114731 (1, 2, 1, 1, 1, 2, 3, 3, 2, 2, ...). Let D be the sequence A114732 (1, 2, 3, 1, 1, 2, 3, 4, 5, 6, ...), E be the sequence A114733 (1, 2, 1, 2, 3, 4, 5, 3, 1, 1, ...) and F be the sequence A114734 (1, 1, 2, 3, 4, 2, 1, 2, 3, 4, ...). Then:

- A upper trims to B

- B upper trims to C

- C upper trims to A

- A lower trims to C

- B lower trims to A

- C lower trims to B

- D gives the number of times each element of A occurs

- E gives the number of times each element of B occurs

- F gives the number of times each element of C occurs

- A gives the number of times each element of D occurs

- B gives the number of times each element of E occurs

- C gives the number of times each element of F occurs

- D lower trims to E

- E lower trims to F

- F lower trims to D

- D upper trims to F

- E upper trims to D

- F upper trims to E

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

E(9)=1 and that's the third 1 in sequence E, so B(9)=3.

MATHEMATICA

c[n_] := Flatten[ Table[{Range[3 Floor[(k - 1)/2] + 2],

     Table[{i, i}, {i, Floor[k/2] + k, 1, -1}]}, {k, n}]];

uppertrim[list_] := Fold[DeleteCases[#1, #2, 1, 1] &, list, Range[Max[list]]];

lowertrim[list_] := DeleteCases[list - 1, 0];

numbertimes[list_] := Table[Length@Position[Take[list, k], list[[k]]], {k, Length[list]}];

a[n_] := uppertrim[c[n]];

b[n_] := uppertrim[a[n]];

d[n_] := numbertimes[a[n]];

e[n_] := numbertimes[b[n]];

f[n_] := numbertimes[c[n]];

b[6] (* Birkas Gyorgy, Apr 21 2011 *)

CROSSREFS

Cf. A114729, A114731, A114732, A114733, A114733.

Sequence in context: A343558 A297877 A027926 * A031282 A085685 A267632

Adjacent sequences:  A114727 A114728 A114729 * A114731 A114732 A114733

KEYWORD

nonn

AUTHOR

Kerry Mitchell, Dec 28 2005

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 2 14:28 EDT 2022. Contains 355007 sequences. (Running on oeis4.)