A114734 One of a family of six fractal sequences that transform into each other.

1, 1, 2, 3, 4, 2, 1, 2, 3, 4, 5, 6, 7, 5, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 8, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 11, 9, 7, 5, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 14, 12, 10, 8, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 17

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..92.

Example

C(10)=2 and it is the fourth 2 in the sequence, so F(10)=4.

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

Crossrefs

Cf. A114729, A114730, A114731, A114732, A114733.

Sequence in context: A037838 A165052 A107474 * A299755 A323907 A214065

Adjacent sequences: A114731 A114732 A114733 * A114735 A114736 A114737

Keyword

nonn

Author

Kerry Mitchell, Dec 28 2005

Status

approved