A114732 One of a family of six fractal sequences that transform into each other.

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

Offset

1,2

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

Vincenzo Librandi, Table of n, a(n) for n = 1..5625

Example

A(5)=3 and that's the first 3 in that sequence, so D(5)=1.

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

Crossrefs

Cf. A114729, A114730, A114731, A114733, A114734.

Sequence in context: A157813 A111879 A193280 * A123338 A152735 A249128

Adjacent sequences: A114729 A114730 A114731 * A114733 A114734 A114735

Keyword

nonn

Author

Kerry Mitchell, Dec 28 2005

Status

approved