A114729 One of a family of six fractal sequences that transform to each other.

1, 1, 1, 2, 3, 2, 2, 1, 1, 1, 2, 3, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5, 6, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 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, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4

Offset

1,4

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..104.

Example

D(7)=3 and that's the second 3 in sequence D, so A(7)=2.

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

Crossrefs

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

Sequence in context: A274884 A076224 A286582 * A186037 A144365 A152197

Adjacent sequences: A114726 A114727 A114728 * A114730 A114731 A114732

Keyword

nonn

Author

Kerry Mitchell, Dec 28 2005

Status

approved